I performed a complete lawn 'rehab' on about 1 acre. I started by going around the property with my box blade, scarifiers set shallow. That did a good job of getting up the 'junk' and starting with the fill process. Remember with a box blade, it isn't a 'back and forth' process, but a 'every which way' process. Drive around like a drunkard looping EVERYWHERE for best results.
Then I spread my 60 CY (4 tandom truckloads) of SCREENED (very important) topsoil where needed, either for fill or to smooth stubborn areas. Don't get refuse topsoil...you'll go batty getting out clumps and sticks.
Again with the box blade.
Going back, I wish I had a York Rake. Would have made removing debris and old thatch much, much, much, much easier. Strongly encourage a York Rake purchase.
I also look longingly at a disc harrows set. TSC makes an "XB" version for sub-compacts and I think that would do a spectactular job of 'chopping up' the top couple inches for amendment and smoothing. It's a few hundred bucks, though, so I haven't been able to justify.
I started with the tiller thing and it is unnecessary. Great for a garden, but just downright painful for lawn rehab.
Get the right starter fertilizer and seed for your situation. Pay extra...don't go to a Big Box. Go to a proper nursery.
I didn't do any lime or other amendments. I did have a 9-zone sprinkler system installed, though, which was critical to getting the seed up. Hit it 3 times a day for a few weeks and it worked like a charm.
The attached picture shows my lawn the spring after my rehab. The grass in the foreground was 'forest floor' when I moved into the house. 3 years and with painfully little care, it still looks nearly as good. I'm overseeding this fall, though.
As far as stability, I just pulled my 5,500# travel trailer onto an area where I filled 18", tires on the ground for 3 days without wood or other support. Didn't even leave a dent.
I hope this is helpful. Don't get too hung up on saving any of your existing grass...just start fresh. That way everything matches.