I think a condo from one of these sites would be great for you. They are typically full week rentals. Redweek.com and TUG2.net are your total price, which is different than VRBO. I should mention that on Redweek.com to actually do the rental and contact the owner, you need to join for the year, which I believe last time I joined was $15 for the year. I usually sign on as a guest and if I see something I want to rent I join and contact the owner, just as you are taking about doing.
What I like about the timeshare rentals too is that all the units have the same furnishings, are on a upgrade schedule, etc. and all I have rented have tasteful decorating. One thing to make sure not to do (very easy to say no) is signup for a resort tour which is a timeshare presentation. They will tell you to go over to pick up your coupon book which is an opportunity to try to sign you up. Don't bother. If you are asked to attend a resort tour and to get a freebie $50, $100, free tickets just say very nicely, "No thank you. I'd rather get a root canal." That line seems to get the point across and they don't ask again. IMHO these are not something to subject yourself to. The resorts are lovely to stay at, have great staff, and great customer service, and I love renting timeshares. Presentations, though, are high pressure, long, and for me the last thing I'd ever want to do on a vacation. Also, I wouldn't want to own one in Orlando either as cash is king and the timeshares are very easy and reasonable to rent (no reason to own one IMHO). Also, if I were to buy one, I'd do it on the resale market for a lower price.
I absolutely love staying at these. PM me or post ones you are considering on this site too if you want some feedback about what other people think. There are so many great timeshare resorts in Orlando -- tons of really lovely ones. Or you could even to a search on this site and probably get a lot of information. Many on this forum rent these frequently for their Orlando trips and I can certainly see why.