Howdy, SEC.
Don't call the Sheriff. TPWD handles boats/outboards, county Tax Assessors do trailers. Getting more agencies involved will only complicate things.
Your best bet is to travel down I-45 from Willis to the TPWD office at 350 North Sam Houston Parkway East, Suite 100, Houston, TX or another closer office. Take any and all paperwork from the seller. They've been helpful when I registered boats in Texas. Hopefully the lien is longer in effect. Bear in mind, no title in Texas is going to run you through the wringer.
Is the Lone Star sitting on a trailer? Your Montgomery County Tax Assessor is the place to go, again with any paperwork.
Take care of the boat first, then the trailer. If worse comes to worst, you can get another trailer. But you can't get another 1961 Lone Star Bay Harbor.
As JB said, don't go spendy fixing her up until you have legal ownership or you might be building a playhouse. Good luck and hope you won't be waiting years for legal ownership.