I'm at level 52 and I've gotten to the point where many of the items I pick up for my inventory are worth more than any of the merchants have? Is there any way around this problem?

fences ussually carry 4,000 gold and if you want to train a skill with a merhcant (like arcadia), the money given to them is added to their inventory so you can "barter" for training

Speech perks are an option. The last one or two involves increasing vendor gold, I think.

That being said, a good option is just to buy up things you need from the certain merchant - potions, arrows, new enchanted gear - then sell off expensive items.

If you have access to Solstheim, Glover and the rest of the merchants carry a decent amount of gold, only if you do not belong to the Thieves Guild. Otherwise, Spech perk is your best way to increase their cash available.