Look into re-creating the logs - if they are lost in a fire or something like that, this is permitted. Basically just certifying that all the ADs are complied with, who cares if it wasn't in annual then, you weren't the owner or the operator, so it wasn't your problem then...
Figure out what ADs there were during that time period, and have your mechanic either re-do them or show that they do not apply because of some no AD replacement that is likely on the airplane now.
The 20-30% reduction can be shown empirically - look at sales price of complete logbooks airplanes vs. incomplete -- I looked at a Mooney a few months ago, it had an attractive price, but it was missing logs from when the owner was in Costa Rica with it or something like that, the broker had it listed easily 20% less than a comparable one.
Incomplete logs to many people is a sign that something is wrong = uneasiness = higher transaction cost = lower price, the bank understands this, they have to hedge against it. They lost their shirts on planes during the recession, especially the sub 100k ones, they repo'd sold and lowered the price of the market due to supply + economic reality. They are coming off a bad experience + new banking regs = need more security...can't fault them for loaning on a high risk asset and expecting some additional collateral.
Another suggestion is to get a different appraiser. Some won't deduct as much and you can generally tell them what ballpark you're hoping for. In my experience, they come pretty close as long as it can be justified (not going to appraise a 1960s straight tail 172 for $100k, but $50 is probably doable). Additionally, it may just require contacting the appraiser and walking them through the missing logs, showing them that everything has been complied with, therefore no deduction in value. Uncertainty = lower price, remove uncertainty, value increases...
