Yes, I can see that it would be better to feed EQ-ed analog audio into the digitizing circuits rather than applying the EQ to digital data, but $1500 just isn’t in my budget right now. Of course, if anyone wants to subsidize my project, send contributions to my email addr. 
If you follow the link to KAB Electro Acouistics you’ll see a dedicated 78 phono preamp with multiple settings for $600 or $675 depending on the option you choose. They have a page showing a discontinued model, (Souvenir Mk 2), but they are selling its update now. If that was more within your budget, you could pick one up, and sell it when you’re done, on eBay, or even to me.
If you play a 78 RPM record at 33 1/3 or 45 RPM into an RIAA phono input and then speed up the recording, the equalization will be completely wrong even if the 78 was recorded with RIAA.
An equalization curve has a turnover point and a rolloff point. The turnover is the frequency below which the bass was reduced when the recording was made (and below which it is boosted when played back). The rolloff is the frequency above which the treble was boosted when the recording was made (and above which it is reduced when played back). Actually, rolloff is usually specified as the number of decibels of equalization at 10,000 Hz, but the concept is the same.
The RIAA curve has a bass turnover of 500 Hz. Let’s say you have a 78 that was recorded with this curve and play it back at 33 1/3 RPM into an RIAA phono input. The RIAA playback equalization will boost frequencies below 500 Hz. When you speed the recording back up to the equivalent of 78.26 RPM (the actual recording speed of these old records), the turnover point will increase also, to 500 * (78.26 / 33.33) or about 1174 Hz. Similarly, the point where the high frequencies roll off will be increased also. The result will sound tubby and dull.
If you’re going to play 78s at 33 1/3 or 45 and then speed them up, it’s best to do the transfers flat (i.e. with no equalization) and then equalize them after you speed them up. Alternatively, you could record through an RIAA phono input, unequalize them (i.e. use an inverse RIAA equalization curve), speed them up and then re-equalize them.
I agree with Askance, fishbicycle et al. that for material like Hank Williams you’re better off buying commercial CDs than doing the transfers yourself. They’ll sound better than anything you can do yourself. Commercial CD transfers are done by experts using professional equipment and the best source material available (usually). I assume that much of Williams’ output was originally mastered on tape, and any reissues that use the master tapes will sound better than anything you could get off a used 78.
On the other hand, if you want to remaster 78s as a fun project or hobby, your dad’s Hank Williams records are as good a place to start as any. I’ve been doing this for years using older material (mostly twenties and thirties) and have built up a collection of home made CDs with stuff that, as far as I know, has never been reissued. When I first started I used common records for source material.