Paint will form a pigmented layer on the table. Friction from whatever you are drilling or cutting will scuff the surface of the paint and will in all probability stain the wood you are using. Paint will never be as tough or hard as steel.
Second problem would be softening of the paint due to...
If the kerf tends to close and make the blade stuck, use small wedges to keep the cut open. And a little candle wax on the sides of the blade will help too.
I used a very similar idea. My main problem was that I used an unsuitable blade. I had a bow saw blade which probably had the wrong tooth profile. You might do better with a section of bandsaw blade, but you would be much better off with a proper framesaw blade. For example...
I made a framesaw for this very purpose, but found it hard to keep the blade straight. It twisted badly and wandered all over the place due to the blade not being sufficiently tensioned in the frame.
Yes, I've used proper beefy ones too. They could certainly do the job. You would have to adjust pressure/distance so that it would remove the outside without damaging the heartwood.
Do the teeth feel blunt? It may well be that the teeth are still sharp.
If you are sawing at a 30 degree angle to the end grain, then as you start your cut you are cutting only a few mm length and progress will be quick. As your cut progresses, the length of your cut increases and the progress...
My experience is that whatever you use, get it on quick. The fresh surface is prone to rust quickly after de-rusting and although it's only a flash rust on the surface, it's dispiriting to see your clean surface disappear.
The watermill in Ivinghoe is just up the road too and tends to open on the same days. They grind local wheat there and sell the flour if you are into baking.
Other attractions in the local area are College Lake which sometimes has green woodworking displays and the Tring museum of dead things...