Oh dang, sorry. Somehow between the time of reading your question I completely forgot 4x4 was desired.
Yes, many people build Slash 4x4 MT. You can easily put larger tires on it, but don't forget to gear accordingly. Often people use 1/8th scale brushless in their trucks. Also, most 1/8 scale MT bodies will fit the chassis, this will give you that MT look.
I have seen some used rollers for sale decked out for around $180-325. A bit above your budget, however, they can be had with full 1/8 systems and teckno / mpi shaft. Usually all they is a radio; of course this is the upper range.
They sell fast and I have missed out on 3-4 deals because of where I live, and other circumstances, (doctors appointments for wife).
One time I priced one out using Towers for Discount and eBay / Amazon and the truck came out to $1125. The man selling it was only asking $350. Only problem you would need to worry about are the diffs being worn out. However, most people selling on this forum are rather honest.