Learn English – “worse” vs. “less better”

Your current account balance is $X smaller/less than is required

It is possible, at least hypothetically, for a "balance" to be negative. A large negative balance is certainly not smaller than a small positive balance, but it is less, by the accepted meaning of the word.

To say that one amount is smaller than another is, strictly speaking, to preclude the possibility of its being negative, or otherwise to assume that one is speaking of non-negative amounts. The word "balance" implies an amount that could, at least hypothetically, be positive, negative, or zero---as balances tend to be explicitly signed quantities, debit or credit in some sense---and therefore to me it does not seem appropriate to say that one "balance" is smaller than another unless one is speaking in terms of absolute value, but even this would not usually be inferred on its own without explicitly making the situation clear.

For example, if A's balance is -$5.00 and B's balance is -$3.00, then both of the following would be true:

A's balance is less than B's.
B has a smaller negative balance than A.

In the original example, without further context, I would only use less than.

I believe you are misunderstanding slightly. If I may rephrase the second quote:

To say that a quality is of a lower degree, you can usually EITHER add -er (one-syllable adjectives) to the end of a negative adjective or adverb, OR qualify it with less (adjectives of two ore more syllables).

To get lower degree you don't qualify the negative with 'less' you qualify the original with less. So for the adjective "pretty" the greater degree is "prettier" or "more pretty". The lower degree is "uglier" or "less pretty".

"More short" is not generally used because "short" is a one-syllable word. "Less short" is also not generally used, but if it were would mean "longer" - i.e. it has less of the property of "shortness", not less of the property of "length".