I assume you have read up about it on the TPWD website?
http://www.tpwd.state.tx.us/fishboat/boat/owner/buying_and_selling/index.phtml
You will need the title signed by the owner front and back and either a bill of sale or a form PWD143.
Is the person your buying the Seadoo from the same owner on the title? If so he needs to file for a lost title.
If he is not and since you don't have the title, you need to find the "owner" that is listed on the title. Have you called the TPWD and give them your TX numbers and ask for the owners name and address?
I had a simular problem when I bought my Seadoo last month. The seller had the title but I needed a signed PWD143 form or Bill of sale by the orginal owner. I got his name and mailed him the forms to sign, lucky he was willing.
You really need to find the owner per the title and go from there.
There maybe other options that I don't know about, but you are right they don't bend the rules up there.
Now on the trailer registration, you can get around that by just saying it's a homebuilt /non-titled trailer.
Per the website; he shouldn't have sold the Seadoo without the title.
"Texas Titles
A title printed in the seller's name is required to transfer ownership of a previously owned vessel and/or outboard motor titled in Texas. Check the Certificate of Number card. If there is a title on the boat, it will be designated "TITLED" on the card. The following forms may be used to replace a lost or destroyed Texas title.
To replace a lost or destroyed Texas title for a vessel/boat, submit form PWD 143M (PDF 405.1 KB).
And by the way it isn't cheap, I paid $190.00 to TPWD to transfer with $2000.00 declared value.
Good luck