I hear a familiar old Mexican tune playing here...
We recently purchased a timeshare in Hilton Head. We received a deduction on the purchase price using our Florida timeshare as a trade in. The purchase documents only show the reduced purchase price. We signed a Timeshare Transfer Agreement with Elite Equity Transfers where we agreed to transfer title of our Florida timeshare to them or "any other entity or person as may be assigned", for a fee of $375 + our resort's transfer fee of $150. They have contacted us requesting payment before the process can begin. I spoke with them on the phone and they say they do not sell timeshares but handle the transfer paperwork ie estoppel letter, court costs, recordation fees etc. I questioned the sales manager at the resort and he said that this was a straight transfer (not a sell of our Florida timeshare in order to recoup money to purchase the new timeshare) and as along as the title was clear and the maintenance fees where paid there would be no issues.
Does this sound like a scam? We have not paid any fees yet.
"Scam" is not really the right word, it's really more just a consequence of a legal marketing and sales ploy.
In essence, you overpaid for
whatever it is that you bought from the developer. The contrived and entirely bogus "trade in value" was just a marketing lure; they gave you
nothing for that "trade in" week (...which, in all fairness, might be exactly what it is worth in today's resale market anyhow). They "reeled you in" by taking the unwanted week off your hands, merely adjusting their (already inflated) developer sales figure accordingly to still ensure a comfortable profit on the developer sale. Similar practices occur in new car dealer showrooms every day. At least with new cars (unlike w/ developer-sold timeshares) there are other, independent sources available (e.g., Consumer Reports) to pre-determine the
real bottom line dealer cost.
Grupo Mayan plays this same "timeshare trade-in" game in Mexico. In your HHI case (unlike the GM Mexican version)
you apparently get to pay the deed transfer costs
out of your own pocket 
. Your "trade in" is almost surely destined to be a "no reserve" PCC ebay auction item in the very near future. Even if it sells there for just a penny, the closing costs you are about to pay ensure some profit for the closing entity; they may well
also charge the "new eBay buyer-to-be" closing costs too, thereby further increasing
their profit.
There is little doubt that you should rescind the overpriced developer purchase if you are still within the SC state law rescission period to be able to do so; your post only dates your purchase as being "recently").
Without knowing the contractual language of your purchase, I'm not sure if you would also need to do anything more (or separately) to halt and reverse halt the "trade-n / transfer" process.
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P.S. On further reflection, if your "trade-in" is already in the hands of a separate entity for "processing", I must assume that you are actually already well
past the SC rescission period. If so, this is already a "done deal" and you now own a Hilton Head timeshare and the "trade in transfer" process is already underway --- with
you pre-paying for future "closing services" (I'm betting that your developer sales contract somewhere
allows for that to occur). If that's the case, all you can likely do now is "pony up" and let them exercise what is likley a "power of attorney" you have already executed, enabling them (and / or any other entity they may work with) to ultimately move your "trade in" into someone else's legal ownership.
Asked another way, why wouldn't "Elite" just prepare one new deed with the new intended recipient as grantee, rather than create this extra deed prep and recording step into their name first? And why has it taken them several months to prepare a new deed if it's now evidently only going right into their own name anyhow? 
