Fairly Simple

:32, skip it: If you take the S8 at :32 past, you'll have to come up from the tief station at the Hbf to the ground level tracks. If you wait for the :47 S9, you can make an easier change in Hanau and get on the same RE.

:47, change in Hanau: An S9 comes through the Regionalbhf at :47 past each hour. This S-Bahn ends at Hanau Hbf, where it is much easier to catch the RE on its way from Frankfurt Hbf to Würzburg. If you leave the Regionalbhf at :47 past, you will arrive in Hanau at :29 past the next hour and have a half hour to catch to RE at :59 past.

You can view the station layout of the Hanau Hbf here. It is important to note that the S-Bahns from the airport always arrive at tracks 1 or 2. The RE for Würzburg always come through the Hanau station on track 103. All tracks are at the same level, but there is a connecting tunnel accessed via stairs.

:02, last sure chance: An S8 comes through the Regionalbhf at :02 past each hour. From the airport it goes through the underground station at the Hbf :013 past. Get off at the Hbf; it's the last station on the S8 route for you to catch the RE to Würzburg. You'll have 17-21 minutes to make your way up to the ground level. There find the platform for your train per the previous table.

:17, worth a try: Lastly, an S9 comes through the Regionalbhf at :17 past each hour. All arrive at the Frankfurt Hbf (tief) at :28 past. Except for 9:17, 11:17, and 13:17, you will have 6 minutes to get to the RE at ground level. You might make it if you hurry and know the platform number of the departing train. You might as well try. At worst you miss the first train and wait an hour for the next one, which you would have to take anyway if you didn't try.

Most complicated

In addition to the S-Bahns coming through the FRA Regional Bahnhof, there are a number of regional trains which terminate at the ground level, just a few platforms away from where the Regional Express leaves for Würzburg. This is the easiest change to make, but it is more complicated as to schedule. Not all regional trains are worth taking, and some leave from track 2 rather than track 1, which requires you to descend a different escalator from the level above the track, so you have to know what train is coming when and on what track. If taking one of these trains, it would be best to board the front end of the train at the airport so as to have the shortest walk at the Hbf.

RE 12125 leaves Regio 2 (track 2 of the Regionalbhf) at 8:09 and arrives at track 17 of the Hbf at 8:23, in plenty of time to catch the RE leaving from track 9 at 8:34. I would pass up the S8 at 8:02 in favor of this train.

RE 12753 leaves Regio 2 at 8:52 and arrives at track 20 of the Hbf at 9:04, in plenty of time to catch the RE leaving from track 11 at 9:30. I would pass on the S9 to Hanau at 8:47 in favor of this train.

From 9:00 until 17:35 (5:35 PM), there is a regional train every hour at :35 or :37 past. At 10:37 and 12:37, it leaves from Regio 2; all others leave from Regio 1. If early enough, I would take these trains instead of the S9 to Hanau at :47 past. They provide at least 40 minutes to make an entirely ground level connection at the Hbf.