AFAIK the stocks are interchangeable on the original 20's, but not on the LT's, which have receivers scaled to 20 Gauge. The first 20 Gauge 1100's were essentially 12 Gauge receivers with smaller barrels and magazines; what you have heard probably applies to those only, not the LT models.
Ask Remington. Their support is good, both phone and on-line. FAQ's already contain some info about the 1100 20 Gauge variants over the years (I think the change occurred in the late '70s).
http://remington.custhelp.com/cgi-bin/remington.cfg/php/enduser/std_alp.php?p_sid=p2aN9spi
Search their FAQs or ask more questions yourself. Also call them with your serial number, and they can tell you exactly what model and year you have.
Something from their FAQ's that will answer your question, AFAIK:
The Model 7400 and Model 7600 are both offered with a Monte Carlo style stock, which allows you to use a scope more comfortably. However, if you wish to change to a straight comb stock, we do offer wood and synthetic stocks which are interchangeable with these models. Current 20 gauge 870, 1100 and 11-87 butt stocks interchange. You may order one of these stocks by filling out a parts order form HERE or by calling our parts department with a credit card at 1-800-243-9700 M-F 9-5 EST.
You can get whatever you want here:
http://www.wenig.com/ Not cheap, but really nice.
Or contact these guys; they're less expensive:
http://www.boydsgunstocks.com/
It's easier to find a Monte Carlo stock labeled "7600/7400" but it should fit on your receiver. Ask Remington to confirm that the LT is the same as the "current 1100"; I think it is, but they know for sure.
But, praytell, why? The LT-20 is such a fine little field gun as-is.