I understand your dilemma, but you are going in the wrong dirrection.
1. Do not slip cover leather.
2. Do not slip cover recliners.
Why? It will look bad. Anyone that says it will look good is either trying to sell you a slipcover, or is simply wrong. The slipcovered leather will not only look bad, but will also feel strange.
For the price of a decent slipcover, go to Craigslist or the Penny Saver, or (my personal favorite) neighborhood yard sales in high- end neighborhoods. The value of used furniture is so incredibly low. It could take some time and effort, but you can find more neutral furniture at terrific prices if you are willing to put some time into your search.
Start laundering some funds from your budget to save for some nicer pillows to put on your new (used) furniture.
Add new pillows, and a new rug....
The rug above is very affordable, from Dash and Albert. When I was single, I purchased an off-white sofa from the Penny Saver for $35. Sure, it didn't look new, but it also didn't look bad. By adding the great throw pillows, you pull the eye away from the sofa's age, and all people see are the pillows.
I recently purchased a Century bedroom set for my grandfather for $200. Do you realize how expensive a Century set is? I once ordered a Century dining set for a client that was over $40,000. There are some good deals to be had out there. Give yourself more than one day. Patience really is a virtue. (I know, I already told you not to get a bedroom set... but grandpa likes it... and it is an excellent quality.... Ignore that part of the story- focus on the good deal on Craigslist)
Stop thinking about what you paid for the furniture. Someone else paid a lot for their furniture too, and now they are are selling it to you.
While you are shopping, keep in mind the rest of the room. Look at this great sideboard:
See the before and after project on Design Sponge.
Finish off the look with some great curtains:
Think neighborhood yard sales in high-end neighborhoods. I also once got four Pottery Barn barstools for $25 each. A current style and color in perfect condition. I also once purchased a Bosch stainless dishwasher for $200. Practically new. Sure, many days I don't purchase a thing, (and now that I have a daughter in swim team, I don't go at all), but if you are patient, you can find good deals. Hey readers, tell us about your good deals. What have you found out there? Inspire Carol!