I assume from all this that the car has not been emissions OR safety inspected in Texas. Based on that, here is how you go about getting it titled as a 1965 under the new rules:
You do not need a DPS emissions waiver nor do you even need to involve the DPS. The MCO/MSO established it as a replica of a 1965 and it is NOT required to have emissions nor pass any sort of DMV/DPS test. It just like registering a new Ford truck in every respect. All you need is your insurance card showing it as a 1965 Ford GT40 and take that card and the car ONLY and have it safety inspected at a local Kwik or Jiffy Lube. I am in Houston and if you are near Cypress send me an email and I will tell you where I have mine done, they are knowledgeable about this.
When you get it to the inspection station tell them you want a SAFETY inspection and show them your insurance card ONLY. You need to have insurance with a replica-friendly carrier that knows how to insure and paper these cars. DO NOT involve the MSO at the Jiffy Lube, its not needed or relevant to them. They will safety inspect the car and if you are assertive and tell the you will drive and they will ride on the brake test, they won't even expect to even drive it. They will enter it into the state DMV system as a 1965. You'll get your inspection sticker applied and a print out. Take that print out, your MCO/MSO, bill of sale, insurance card and checkbook back to the
tag office. You said TXDOT below but let's be clear, you need to go to one of
Don Sumner/Harris County Tax Assessor offices where normal vehicle licensing takes place. (If that's what you meant, no biggie, just clarifying that you do not go to a TXDOT office.) Take the VIN pencil trace as a backup, but your MCO/MSO is the operative document for this transaction. Now because you have already sort of created extra work for yourself with your first visit with all those VIN issues, if it were me I would just go to a different county clerk/tag office. Walk up to the glass and tell them you want to register that car. They'll pull that same inspection record up in the state DMV database and it will appear as a 1965 FORD GT40 using your ERA VIN. Once you are at that stage, tell them you understand that car is eligible to be registered as a 1965 and see if they will proceed under the new rules. If not, then take the ASVE route and then when your renewal is due next year walk in and apply for a title conversion under the new rules and they will grant it. I stopped by my local office and asked them about switching my 2009 ASVE to a 1966 title and they said it was easily provided for under the new rules. However, I learned I'd have to surrender my 1966 plates and run new plates so I said no thanks. Having it titled as a 1965 will not make it worth any more money.
EDIT>>>Not discounting what Sammy wrote above, I am just relating how things have worked for us here in Harris County.