Recently I removed the transmission from my Lincoln and had it overhauled.  He went through both the tranny and the torque converter.  The issue I'm having is with the installation.  The tranny won't slide all the way to the bell housing.  I have a slight gap all around and no matter how much I work it.  It will slide forward when I tighten the 4 bolts but when I loosen them the gap returns.  The bolts do tighten without very much effort.  

Am I good to go or do you think I have an issue?

My guess is that the tangs on the converter are not aligned with the slots in the front pump.  Turning the engine with this condition will destroy the front pump.  I would suggest that you determine where the slots and tangs are, and either turn the engine or the pump gears until they align and try installing the trans again.  If it won't slide in, try again.  Failure to get them aligned and running the engine will result in destroying the pump and sending cast iron grindings throughout the transmission.

John - "The Hoosier Hurricane"

ruined a transmission in my younger days this way.

I'm kind of resurecting an old post but I just wanted everyone to know how this ended.  I had this tranny in and out of the car maybe 6 or 8 times trying to figure out the problem.  It would slide in with about a 1/4 inch gap between the tranny and bell housing and the motor would not rotate when I tightened it up.  I never tried turning it over with the starter just with a bar on the crank or the torque converter.  I tried putting installing the torque converter and housing first and then the tranny as a complete assembly.  No change.  The gap just changed from the tranny/housing to the housing/motor.  I could not figure it out.  I went and discussed this with my tranny builder.  He offered to stop by and take a look at it.  He thought it was just a problem of getting everything to line up.  That was about a month ago and, due to his and mine schedules, kept getting pushed back.  

So yesterday he and one of his techs had an opportunity to stop by.  I showed them what was occurring and he checked everything over.  He initially pulled the from pump, just 4 bolts, to check it out.  It was fine.  The splines on the front pump were slightly chewed up so he felt that was the problem.  He then loaded up the tranny and the t/c to take back to his shop.  About an hour later they called.  They had located the problem.  I asked them if it was the t/c and yup, it was.  The sprags and/or the stator were in backwards keeping the tranny from sliding in all the way.  We test everything and it fit perfectly.  It took me maybe 2 hours to put it all back together.  I slid it in, lifted the tail housing and jiggled it and it popped right in.  Just the way it should.  It's a heavy bastard though.  

It was a simple error and easy to fix.  These guys have been around for a long time and, in my opinion, the best.  Things do happen.  I'm just glad I recognized the problem and knew to stop and figure it out.  Now to just get that damn starter back in.