I don't think you'll have a problem.
Arrive on Delta at 09:40 and all being well you should be out of the airport by 11:00-11:30. As has already been said, you clear customs and immigration at LAX and can then either go straight to the departures area or walk out of the terminal and come back later with your boarding pass for your MCO flight and just go straight to the security check.
For a 23:20 domestic departure on DL to MCO, and as you should already be checked in and have a boarding card as a result of checking in for our first flight, you should be aim to be at the Delta terminal (terminal 6 I think) no later than 22:00.
So at worst case that should give you ten hours land side in the LAX-area.
This topic outlines the process for finger printing (and a lot of other things) for flight training in the US:
http://www.pprune.org/private-flying...-part-1-a.html
It seems to suggest you need to go to a Sherrif office to have your finger prints taken... Have you worked out where you can go to do this near LAX? If so and it's nearby, great. If not, find out exactly where you have to go and try to find something near - traffic around LAX can be VERY bad at times, particular in the morning and from mid-afternoon to evening, so the nearer you can do this to LAX the better.
All being well though and if there's a location you can have your finger prints taken nearby to LAX, there shouldn't be an issue with arriving, clearing immigration, getting the finger prints done, getting back to LAX, spending a few hours in a hotel and still making your MCO flight.