Thanks again - I am taking them in to my optician tomorrow! I'll report back with the solution we achieve!
If your distance acuity is off, as an optometrist the first things I would be thinking of are the prescription and the lens centring. Getting a recheck is the right move.
The quality of the lenses is more important than the brand. The major manufacturers produce a large range of progressive lenses at different price points. As CC mentioned as a general rule you get what you pay for. The cheapest lenses may be decades old designs using traditional grinding methods which have optical limitations. Newer (and more expensive) designs use digital surfacing (CNC) which allow better control of aberrations and optimisation for the prescription, the frame and how it fits, giving sharper vision, reduced distortion, better reading areas and easier adaptation.
You are not just buying a pair of lenses, but also expertise. Your eye doctor or dispenser are familiar with the brands of lenses that they use. By all means discuss with them which model of lens is most suitable for you, but asking for a brand which they are unfamiliar with may be a recipe for trouble.
So, I took my glasses to the optical shop and she volunteered to courier them to an outfit that should be able to add feet/pads to the frames, lifting them off of my face. I'm not sure how this will pan out but we'll see!
You were right, @CityConnection - the feet couldn't be screwed onto the frames, so silicon pads were the solution suggested. I'm wearing them today and hoping they help to alleviate the digging-in feeling.