On my old 1963 mk1 I used yoko A032 tyres on my steel rims like yours. Didn't have any problems with them. Trouble is a they don't look very period, but grip really well!!
The A032's are really hard to get here, and pretty expensive as well. The A008's can be ordered at pretty much any tyre shop, but the A032's are only available from one national motorsport supplier (or you can import them yourself from the UK).
What about Dunlop R7s. They are 165s and have a more traditional tread pattern
They do look really nice, but they are really expensive too.
Here is the abridged leaky tyre saga:
-I bought the wheels with 165 Bridgestone tyres which were a bit old and were run tubeless. I removed them to repaint the wheels
-Got the 145 tyres put on at tyre shop 1 with inner tubes (they wouldn't do tubeless)
-Had a flat tyre the next week from a pinched tube during installation. Got a new tube
-Got two flat tyres a few weeks later
-Shop 2 installed some valves for me
-Valves were too small for the holes in the rims and tyres deflated so I had a bigger valve installed which worked fine
-One of the tyres that still has a tube had a flat
-Shop 2 wouldn't install valves anymore so they put another tube in
-Another flat tyre last week...
I'm sure they'd be perfectly fine if the tyre shop would install them tubeless with the correct sized valve. That's proved to be a real challenge though!
Adding on top of the tyres being leaky is that they are getting pretty low in tread too. I'd already decided that when the tyres ran out of tread I'd replace them with some A008's. I'd also decided after the flat I got last year that if I got another flat tyre I'd replace the steel wheels with something else...
I'd always like these wheels so they seemed like a good option and they fit the car really well too. There's lots of photos of them on page 7 (the tyres don't have enough tread to use at the moment).