was wondering if there's anything 'wrong' with using the following combo
There's nothing wrong with it per se, but there's no reason to use all three finishes.
"Danish oil" type products1 can be used as finishes in their own right, as of course can Arm-R-Seal or High Performance. So the only reason to use a straight oil or blended oil finish first would be if it gives you some benefit. On many woods there's so little visual difference that it's just not worth the extra step and the added wait time; and frequently there's no improvement in appearance at all. As for the shellac, it's simply not needed here since oil-based polyurethanes are fully compatible with "Danish oil".
So in short, you can apply oil-based varnish over "Danish oil" if you want but just applying the varnish straight onto the wood may yield almost the same, or even identical, results with one fewer step.
Incidentally for ease of application and greater assurance of a good result (virtually foolproof in fact) I would suggest converting the varnish to wiping varnish and applying it that way. Read more about that in this previous Answer.
I'm going to try this out on some sample boards, of course, but was reading up and trying to see what would give the best durability with the Danish oil first coat.
Good to hear, it's always a good idea to do samples first. Not testing finish before committing to your project pieces can lead to poor, occasionally disastrous, results even when using finishes you have used before so it's absolutely vital when using a new finish or finishing procedure, or you're working with a wood you're not familiar with2.
So IF you can see an improvement in appearance using the "Danish oil" first it's worth noting that straight linseed oil3 will in general give an even more noticeable change. It's for this reason that I occasionally oil first, and then apply shellac or varnish on top for gloss and durability. If I use a finish similar to commercial "Danish oil" it would typically be the entire finish.... to my mind there's no reason to use an oil/varnish blend otherwise.
1 These are typically a blend of oil, varnish and lots of solvent. Incidentally I always put this in quotes because it's not from Denmark and actually has no real link to the country.
2 A great example here would be if you're used to staining and finishing oak and like the results, then use the same process on birch without a test first. To say the difference in result would come as a surprise is a huuuge understatement!
3 I mean boiled linseed oil (BLO) here, not raw linseed oil. Raw oil is usable here but takes too long to 'dry' to be practical.