ok, I already have my part66 license, but I did what you are mentioning to get an extra type rating.
I learnt the aircraft, took the theoretical exams and passed. After that I worked unpaid to get on the job training. Got all ATA chapters covered and signed by the company's quality dept. Et voila, new type rating added. Similar way to get your initial part66 license.
But bear in mind: a part66 is not valid without type rating. So what I would do in your case:
1/ pass theoretical exams for B1
2/ go to a part145 company and begin working as unlicensed engineer
3/ after a few weeks of experience on type, you go to the CAA and ask your A license.
4/ do your theoretical type rating course and experience at the company, and 2 years after getting the A license I believe you can demand your B1 with that valid aircraft type.
Also good to mention that learning in a part147 and doing experience via a part147 is the shortest way.
You'll not struggle to find an unpaid position, you'll not even struggle to find a paid one. But for that last option, I'm sure there will be other guarantees needed from you (e.g. pay them back if not succeeded and sign to stay with the company the next 3 years was in my case)