Front IRS and rear hotchkiss was the normal standard on virtually all American and a lot of British and European RWD cars from the thirties through to the early 90s and as mentioned by Greg, can work very well.
18" wheels are certainly NOT a traditional or classic hot rod look.
7.50 is not narrow.
As mentioned earlier, different tyres have different response rate or reaction times between steering input and chassis reaction due to different sidewall to tread distortion shape, time and degree. This happens to some extent even with fairly similar tyres, and can be used as a tuning device, but it requires experimentation.
I would keep the tyres as similar as possible, with maybe a smaller tread width relative to rim width on the front so as to reduce sidewall flex and keep the steering crisp.
In my limited experience, especially compared to Greg or CapriRacer, I would consider:-
Same tyre, different width a minor and predictable and obvious change.
Same tyre, different profile, a slightly greater difference but also predictable. Obvious is changed sidewall flex re degree, not so obvious is slightly changed response rate.
Same structure type, different tyre, varies from very similar to significantly different to the point that it is a full time job just driving in a straight line. Obvious differences are tread pattern, but differences in reinforcement fabric structure and placement and rubber compound type and placement are the not so obvious differences that can have a profound effect.
Different structure type. Differences are obvious and predictable in nature but not in magnitude..
Different tread width to rim width relationship. Difference is fairly obvious and predictable.
I would buy a suitable front tyre that has the desired rolling diameter and driving qualities, then buy something compatible for the rear as the rear choice has greater freedom due to being covered.
If you want more cornering grip with the rear with a hotchkiss, you can bend the diff to give some negative camber, but that reduces tread wear life and reduces drag racing traction and reduces straight line braking performance.
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