well, I may have some good news for you (seems you could use some lately).
working in construction I know many people with tax problems. some of them have gone over 20 years without filing, and claiming max. dependants on their w4 forms. (we change jobs often, sometimes 15-20 w2's for one year, so you can get away with claiming way more. usually upto 'married and 9' before it raises a redflag with the IRS).
anyway most of these guys have settled in the last 3 years. some have owed more than 200k and got out of it for about 10k.
so basicly if they are convinced that-
1. what you are offering is the most they will likely get.
2. you honsetly intend to keep your taxes straight in the future.
and
3. to push you farther would just make you give up and stop earning recordable moneys.
they seem to be in a settling kind of mood the last couple years.
I don't no anybody who has made a reasonable offer in good faith, that wasn't able to work something out.