EAC's offset test says "None" for overread.
dBpoweramp reports a read error also and aborts ripping the rest of the track.
Back to EAC, I tried extracting a range that included index 1 of track 1 also, which didn't help. I noticed that the location of the silence was slightly different (by ~10 frames) as well as the duration (25 vs 21 frames) depending on whether burst mode or secure mode was used. It was consistent, such that any 2 burst rips would always turn out the same, for example. Then I tried unchecking the "Drive is capable of retrieving C2 error information" box, and for the first disc this still resulted in 21 frames of silence (although again in a slightly different but consistent location). When I tried the second disc the whole thing came out bit-identical to the rip I'd done on my Pioneer drive

!
So I kind of figured that the drive was behaving differently around this area depending on which sector reading started at. Then I thought to try CDex, which with default settings had some silence also. I looked through the options, where I noticed that the number of sectors per read was configurable. I changed it to 1, and sure enough it was able to read the HTOA on both discs identical to my Pioneer rips

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I'll describe what has to be done in CDex for any others with this drive since it's not quite straightforward. First, in the drive settings, uncheck "Enable Jitter Correction" and set "Read Sectors" to 1. Then select "Extract a section of the CD" from the Convert menu. Make sure the Start Position and Stop Position are set to the first track. Now, for the Start Position, it has to be set to a negative value, but CDex won't allow you to type this in normally. However, if you type a negative number in Notepad or something, you can paste it into CDex. Just come up with a negative number longer than the length of the HTOA, e.g. one of mine was a bit over 2 minutes, so I typed -3 in Notepad, then copy and paste that into the minutes area of the Start Position. You can leave seconds/frames at 0. For the Stop Position which is inclusive like EAC, you'd want it to be 0 min 0 sec -1 frames normally for the rip's length to be correct. However, since CDex doesn't support sample granularity for offset correction, you can set the Stop Position to 0 min 0 sec 0 frames to get some extra samples. Click OK and it should rip fine. Then you can correct the offset by trimming 6 samples from the beginning and 582 samples from the end in an audio editor.
I wonder if Andre or spoon would be willing to add an option for the number of sectors per read...