Old headset on a new frame

Bike noob here doing a project - throwing parts from an old 80s road bike onto a new (chro-mo) frame that I bought from a local bike shop.

Both use 1" threaded headset, but I'm having a heck of a time fitting the old headset head races (cups?) into the headtube on the new frame. I was using the block of wood and hammer method (I know not preferred but..) and I try as I might I couldn't get the cup all the way into the tube. I got it so it was about 2mm from flush and reasonably "level" but took it out.

I went to buy a new headset (from a different shop), thinking the old one might have for whatever reason been slightly larger than standard, but I got the shop to measure both headsets with calipers and the outer diameter on the new one was actually slightly larger, so that won't work.

Also the fork crown race doesn't sit very snug on my new fork, it could move freely.

Someone suggested the new frame might need to have the headtube milled out, but I'm a little unsure why the shop would have sold it to me like that.

From my understanding I have a few options:

1. Take the frame back to the shop I got it from and have them mill out the headtube (probably at some cost to me).

2. Use a semi-circular file and file in inner head tube myself until the headset fits.

3. Get the headset in as far as I can (it seemed like it would work it just wasn't "flush") and tighten things up as they get seating during riding. Seems like a bad option?

4. Try to find a new headset that will fit / just pay LBS to install one.

Any advice?