You can certainly use deeper as the comparative of the adverb deep. It was good enough for Milton (‘That they may stumble on, and deeper fall’), and for other writers too.
That said, the sentence as a whole doesn’t sound quite right. For one thing, it's unusual to follow wisdom of with a noun in that way, rather than with the -ing form of a verb.
I don’t know where this myth got started, but adverbs and adjectives form inflections by degree in precisely the same way. There is no difference at all.
- They pushed harder, faster, and deeper that day than ever before.
- Our team worked hardest.
- Their drill delved deepest.
And it isn’t even the case that there is some rule that somehow exempts ‑ly modifiers — be they adjectives or adverbs, it doesn’t matter — from inflections of degree. They take either more or -er for comparatives, and either most or ‑est for superlatives. Watch:
- I showed up earlier than he did.
- I got here earliest.
- He got here later.
- I have curlier hair than you.
- One is the loneliest number you’ll ever know.
Also, onliest has a long history, although it is now mostly confined to dialect.
And there is absolutely nothing whatsoever with saying:
- He ran faster than any of us that way.
No one, but no one, can ever say a word against against it.
Edit
Here are more examples of comparative adverbs.
Given that this is an adverbial use:
A man walks clean if in a foul way he contract but a few spots of dirt.
Can he then not walk cleaner? Similarly here:
The riches of the East expended that they might sleep soft and wake in magnificence.
Can they not sleep softer that way?
Consider this laughter:
I shouted ‘hurrah’, and laughed loud and long.
Can I not laugh louder and longer?
Can a joke that falls flat, if retold, fall flatter?
If one day you’re sitting pretty, and things get even better the next day, couldn’t you be sitting prettier?
Could you not be harder-pressed to do something today than yesterday?
Consider these adverbial uses of dear:
- 1807 Byron Ho. Idleness, To E. N. Long 99 ― The dear-loved peaceful seat.
I shall soar higher tomorrow than today.
- 1822 Scott Pirate xix, ― That knowledge, which was to cost us both so dear.
& 1833 Ht. Martineau Cinnamon & P. vii. 124 ― It must do without some articles··or pay dear for them.
If you paid dear yesterday, and dearer today, and paid dearest tomorrow, those are all normal inflections.
I could go on all day, but surely it is clear by now that there has never been any general “rule” forbidding inflecting adverbs by degree.
(Sure, there are some adverbs that you just don’t do that with, like now for example, but that is a wholly different matter. It is hard to be “nower” simply because now does not readily admit inflection by degree. But even for that one, you could probably put together a situation where it would somehow be understood.)
Best Answer
One may read quite a bit (here or on this site, for example) and gain some perspective on comparatives and superlatives. But, shucking down to the cob, there seems only two important concepts that govern:
1
2
A Google Ngram seems to confirm that English writers are more shy of writing "tenser" than "more tense". In the case of the adjective "tense" there may well be a psychological factor involved in choosing "more tense" over "tenser". That factor may well be the desire to be understood.
Compared to "tenser", "more tense" is fairly straightforward and easy to understand. In the minds of English speakers, "tenser" may seem easy to misunderstand.
"Tenser" might be understood as something unrelated to the intended meaning
As to whether "tenser" or "more tense" should be used, I'd vote for "more tense". Beyond that, I would not use "tense" as an adjective. I would use another adjective, or a construction employing the noun "tension". Any "rule" concerning single syllable adjectives is only as good as users will accept.