I wouldn’t worry about having more than one type of ISA open at the same time.
I don’t know about the transfer process, generally with cash products its a cheque from one firm to the other (Halifax hand write theirs )
However I do know about the ISA setup. You can have as many ISAs of any time as you want. The issue is funding in the same tax year, that is what gets you into trouble.
2018 you fund a help to buy ISA with bank A, in 2019 you open a help to buy ISA with bank B and stop putting in money in Bank A. This is completely fine
If in 2019 you open a help to buy ISA with bank A and bank B but you only put money into Bank A. This is totally fine
If in 2019 you open a help to buy ISA with bank A and bank B and put money into both of them. HMRC will have some very interesting questions for you at the end of the year.
Help to buy ISAs is the first time HMRC have really gone all out with the API approach, so technically doing the transfer of which is your main HTB ISA shouldn’t be an issue, the only problem is HMRC haven’t finished all the APIs!
My guess is the transfer will be fairly manual and will lots of issues around the technology about who is the owner of the HTB ISA (they tried to make it fancy to stop duplicates and stuff.)
Personally I’d open the new account but don’t put any money into it. Then use their online help to kick off the transfer as I don’t know how much they could do inbranch.
If they force you to fund it then you will have to speak to them first and get some help!