Does anyone have experience with buying a car back after it was totaled in an accident? 

There are too many after market parts to lose to scrap yard.  I doubt they are going to give me much for my Sidekick Sport, even with all the upgrade receipts.

I found another Sidekick Sport with no suspension under it.  The body is straight, with zero rust.  I can swap the undamaged parts to it and be in pretty good shape.

Hello.
 I think it varies from state to state and insurance company to insurance company.

That being said, it is pretty straight forward in most ceases. Here in CA they total the vehicle and pay you out.
 At that point tell your adjuster that you would like to buy it back. They give you a price that is pretty much scrap price. Yes u might be able to haggle a bit on price...again it will depend on the company.

They issue you a salvage/total loss tittle.

when my first tracker got written off (I was in Canada )and an American pulled out in front of me and they wrote it off I bought it back for 125 bucks and they just took that off of price for pay out . they tried to haggle with what they were trying to give me and they were going off craigslist in 3 different states. and that with statefarm insurance

Ya here in Oregon when one of mine got wrecked I had the opption to keep it , it was $225 for the buy back

I bought my wife's 4-door that was totalled from a deer hit here in Colorado. Paid the guy $1000 for it as is, he got a check for like $3k from State Farm for it + my $1000 so he was happy. I worked at a bodyshop at the time so I was able to get it fixed on the cheap. Put roughly 2k into it to get it back on the road. Absolutely love it

Thanks everyone.  I haven't heard back from their insurance company yet.  The holidays and the fact that they couldn't find her to verify the incident....

My major concern is the time to do the swap and I will be doing it by myself.  I travel, a lot. This leaves very few days to work on things for fun.  This is even more so, because my house is nearly 100 years old and I have several projects lined up for it too.

I spent a lot of time and effort getting the parts I wanted.  Letting them go seems such a waste.  The roof rack, Aussie header, and the snorkel, were not easy to get.  I would hat for the snorkel not to at least go to another forum member with a J20 or J23.

A few years back when my Tintop Sami was rear-ended, the insurance company chose to scrap it. There was no frame damage, just a bent gas tank and a wrinkled rear door. I opted to keep it, so insurance looked around for the going local rate for Samurai's (Wa state) and found (at the time) only a few stock Sami's, so all said and done they paid me $2200, which I thought was fabulous, and thus allowed me to begin the YJ SPOA upgrade  Was a very good deal for me, but I think that may be fairly rare overall.

Sorry to hear you lost your Sport.  It was a good looking little truck and I know you had put a lot of time, upgrades and improvements into it.

Thanks nprecon. 

I have been offered 2k to write it off.  I can keep it for 350.  I would enjoy building a new one, but time is a major issue with all my travel.

I will know more in a week or so, when I get home.  I am in DC for all the inauguration chaos this week.