Hi tsoileau,
I would think you could cover the tile with laminate flooring. I take it the slide damaged the vinyl in the stove, refig area on your Big Country. First you need to repair the roller or what ever caused the damage of course. I have a BH3055RL and installed the laminate without any problem. This is the second one I have had and put the laminate in and I installed the laminate on top of the vinyl, did not remove the vinyl flooring. The first one I put the good stuff in, 1/4 or 5/16" thick laminate. The slide would roll on it and made marks, not to bad, but you could see it. On the newer, 08 that we now have, I shopped around and found some cheaper laminate at one of the discount lumber places, only guaranteed 20 years, not 25, but it was only 3/16" thick. So I used that in this unit, looks great, just as good as the expensive stuff, was easy install and the slide does not contact it, except at the furnace vent, you can see that the roller rest on it when the slide is in. But that is not a problem.
Have fun.
Jim M