Crumpite:
I too am living in south eastern MI and I heat primarily with wood. I too use the typical 4.5 cord of wood per season, although some like last winter were milder than ever... Doing the math, 1 cord of red oak has 24MBTU so the season total is close to 108MBTU. The heating season is about 5.5 months long, so that equals about 165 days. Dividing 108MBTU by 165 to get the average yields 654.5k btu/day (average). The coldest days could be double or triple the average with mild days at both ends of the season. Dividing 654.5k by 24 yields about 28kbtu/hr 24/7 (average). I know this is about right, since I heated through a winter with a corn stove right before the price became ridiculous and that stove ran 24/7 putting out around 20-30k btu/hr.
Looking over my utility bills, I typically don't use over 600kwhr/month, unless my wife runs an electric heater in our basement. Our present home does have forced air heating and in the basement the ducts are in the ceiling and with the upper floor wood heated, the central heating never turns on unless we are away for days at a time. So the result in that the basement is cold in winter. So my electrical needs if using a genset with 5kW output to provide direct power as well as charge batteries would need to run less than 4 hour/day. Typically, engine thermal efficiency is about 1/3, so producing the 20kwh of electricity also creates an additional 40kwhr of heat or 40*3412.3 = 136492btu of heat. It is unlikely that more than 85% of this heat is recoverable, even with a condensing heat exchanger on the exhaust, as well as coolant and oil heat exchangers. But that would still yield 116kBtu per day or 18% of the average amount of heat needed for the season. OOps, looks like that misses the requirement by a mile.... For each additional hour run, using electrical heaters, one gets an additional 50% more heat on top of the 116k so doing a bit of math, it looks like I would have to run a total of 7 hour/day, have solar heat collectors, burn more wood or a combination of all of them.
In operating cost, looking at the specs of the Yanmar 2TNV70-PGA engine, they list specific fuel consumption as 0.51lb/bhphr. That is only 27% thermal efficiency and may be due to parasitic losses due to the radiator fan, water pump and other accessories. Not using the majority of the accessories in a CHP application may improve the efficiency substantially, particularly at higher RPM where the fan and alternator can be energy hogs. Thus for 7hp shaft power (I'm guessing here) and 7 hour run time one gets 7*7*0.51 = 25lb of fuel. Since diesel is 7.09lb/gal that translates to 3.52 gal of fuel and about $10.57 in 2010 diesel fuel cost/day or about $317.22/month. I currently pay my utility about $25/month for the privilege of access to electricity and NG before I have consumed anything. I presently spend about $600/season for wood and my actual utility NG and electricity bills usually drops to $80/month with the exception noted. So total utilities and heat (in winter) run around $200/month in town. The only catch is the $400/month property taxes which won't go away no matter whether I lose the grid connection or my job (which has been a popular trend the last 10 years in MI). So taking taxes into account one would be ahead about $300/month despite the higher energy cost of running off grid ($130/year tax is typical in Custer county CO, less if you are zoned agricultural, like leasing your land to a rancher for dry grazing of cattle).
So, if I was designing for this climate (which I'm not, I am designing the system for Southern Colorado), I would size my system for the "average" consumption and supplement with wood heat/direct solar gain and Solar collectors as needed on the coldest days. So the co-gen source would have to be capable of generating just shy of 654.5k btu/day or about 27.27kbtu per hour (averaged over the day). I prefer hydronic heating to forced air, due to the reduction in dust, noise and drafts, not to mention avoiding the huge ducts all over the place. It is also possible to individually adjust each zone to as warm or as cool as needed. For radiant heating the water temperature needs to be 90-125F, whereas for baseboard or radiator style heat exchangers it is typically 160-200F. The higher the temperature, the less efficiently one can recover waste heat from the engine coolant, oil or exhaust, since heat exchanger efficiency drops to zero as the warmed storage fluid approaches the temperature of the source fluid. Given that 90F is the lower limit for getting radiant heat exchange to work, the upper limit depends primarily on the desired level of heat recovery, as well as the space available for heat storage and the desired heat losses from the heat storage tanks (heat loss is higher at higher temperatures). Generally speaking, most mixer valves have an adjustment range of 100F but in the interest of efficiency it makes more sense to stay well below this differential. My plan is to keep the differential closer to 50F, thus 90-140F. This requires more fluid, thus more space than living with 90-190F, but one would have a harder time insulating the tanks for 190F when they are likely to be buried deep under the concrete floor slab. It also turns out that the 90-140 range matches solar collector characteristics very well (they typically max out at around 130F).
So, assuming the lowest limit of 90F for radiant heating, the volume of heat storage water would have to be able to absorb 654.5kBtu without raising the temperature of the fluid more than 50F is calculated as follows: 654.5kbtu / 50 = 13klb of water or about 1600gal. So my plan is to use 400gal tanks (rectangular in section, they look like this:

). Using 4 separated tanks gives one more options regarding how to run the system. One can isolate them all and start the season with just 1 tank, until the depletion rate gets on the high side and then open the valve to the second tank, which will require a longer run of your heat source to "re-charge" and continue in this fashion through the season. A small PLC could handle the logic and math to determine how many tanks are needed, based on the average temperature drop in the heating loops. The bigger the drop, the colder it is outside... If one has solar collectors, they start the day heating a different tank to the one used by the co-gen system and if the temperature differential of the collector drops below a determined point, the PLC switches over to the next tank. The rectangular tanks are easier to insulate using flat rigid foam insulation, whereas cylindrical tanks need to be spray foamed.
I have probably left out a few factors in my concept, but it certainly seems feasible to live off grid based on this kind of system, without huge expense. Depending on location, if wood is plentiful and cheap and sunlight abundant, one may want to reduce dependence on the generator and install a PV array and use solar collectors to best effect. Provided one does a DIY instalation, the cost is modest when compared to other costs incurred in building a new home (kitchen, bathrooms, roof).