Going by your last pic, the engine mounts seem to be for a TC.
The S1 / S2 engine mounts (RHS of pic) set the engine a little lower.
The tilt is puzzling.
The front RHS of the engine does sit quite close to the chassis leg but yours appears a tad closer than I remember.
While your chassis looks pretty schmick, I'd treat it as an unknown and use / fabricobble a set of long trammel bars so as to measure where everything is located. I see this is a judicious precaution because half the rear suspension hangs off the gearbox and relies on proper placement of the engine/transmission for correct thrust angle among other things.
I'm going to take a wild shot that there are 2 different engine mounts installed; there should be no reason to honk out holes larger on the engine mounting brackets to get the engine set in the frame properly. Set the frame level side to side on sawhorses or the like. Measure from the point where the frame transitions from the Y to the back arms down to the floor (assuming the floor is level). They should be equal. Measure from that same point on the top of the frame diagonally back to the end. You should be equal +/-. Measure from the end of the frame to the flat floor. Same? Yes? You don't have any twist.
So now it becomes a question: are the two mounts the same? Take the engine out (if not already done...at this point, should be a 30 minute job...). Examine the mounts. Are they the same? Are they collapsed (i.e. are the vertical metal plates sagging down and not as they appear in the photos?) For the Europa S1 and S2, on both sides, the mount P/N was originally listed as 054E6000. Early cars originally used 026E0374 (which is the Elan part # based on the 26 prefix) but this was changed by Lotus as a running change, and all cars were to be retrofitted with the upgraded Elan 026E6011 mount. (First photo). In any case, it's false economy, at this point, to reuse what may be 50+ years old rubber mounts.
If you have a mount that looks like the second photo, someone somewhere along the line used a later TC mount (074 prefix) on one side. They are different from the 026 mounts above. The shape of the base will tell you whether you have the right mount.
If all the measurements are within specs, then using the proper mount(s) will get the engine set in the frame the way it's supposed to be without having to enlarge holes or some other bodge to get it to work.