There's no implication that the fee being doubled means anything other than that you pay double the amount for the same service.
This was my point. The thing being doubled, qav'ap, is the amount to be paid, not the thing being paid for. Therefore, the object of DIl in ghajwI'vaD qav'ap le' yIDIl is still the amount paid, not the thing being paid for.
The thing being doubled, {qav'ap} (the rent, or rental fee), is not what one would normally think of as being "paid for" *in English*, because English distinguishes between paying "for" some things versus paying (no "for") other things (typically a debt, bill, or fee). Actually, English is inconsistent because you *can* say "pay for" rent or a fee in some contexts, such as "I'll pay [for] your rent", "I pay [for] my children's phone bills", "I pay $500 [for] rent", but you normally say "I pay rent" instead of "I pay for rent" (unless it's in a context like "I pay for rent and you pay for utilities").
In Klingon, {DIl} appears to be the verb one uses for both paying for something (to obtain it) and paying (for) a debt, bill, or fee. The object of {DIl} is the *reason* you're paying. It's just that English adds the preposition "for" in some cases but not others. What you pay out is then the object of {nob}. In *Klingon*, one "pays for" ({DIl}) the rent, just as one "pays for" food.
When Okrand wrote the English definition of {DIl}, he was being succinct in defining it as "pay for". That just means that the subject is paying, and the object is the reason for the payment. It doesn't mean that {DIl} is used exactly in those situations in English where "for" is used with "pay" and not otherwise, which English is somewhat inconsistent about.
AFAIK, those definitions were not provided in the game, but is someone's guess at what the word means. (That guess may well be right, but they go beyond what's actually necessary to explain the usage in the game.) The game itself is consistent in using "rent" for {qav'ap} and {nob} as the verb to pay out an amount: {qav'ap DIl}, but {vaghmaH QaS nob}. It *may* be that you could say {vaghmaH QaS DIl} to say "pay out 50 troops" (rather than "pay for 50 troops"), but that is not how it's used in the game. In the game, you {DIl} a {qav'ap} by {nob}ing some amount of {QaS}.
But here you make a good point that convinces me not to use DIl to mean "pay (money)." Klingon apparently makes a distinction between price as a specified amount, like wa''uy' DarSeq, and price as the idea of an amount demanded, requested, offered, or agreed upon, called qav'ap.
I think you're making this more complicated than it has to be. The object of {DIl} is the reason you're paying something (whether it's an amount or not), and the object of {nob} is the thing you're giving out (whether it's an amount or not). You *can* state an amount as the object of {DIl}, but it would mean that you're "paying for" that amount (i.e., you're paying in order to obtain that amount).
{vaghmaH QaS vIDIlmeH Duj vInob} "in order to pay for 50 troops, I give a ship", "I pay a ship for 50 troops", seems to me to be a pretty clear sentence with no confusion as to what I'm paying out and what reason I'm paying (what I'm paying for),
{qav'ap vIDIlmeH wa' 'uy' DarSeq vInob} "I pay one million darseks for rent"
{wa' 'uy' DarSeq vIDIlmeH qav'ap vInob} "I pay the fee [cost, price, value, or whatever {qav'ap} means] for one million darseks". That is, I'm purchasing one million darseks, and I'm paying out an unspecified {qav'ap}, perhaps a billion Federation credits (or whatever the exchange rate is).
I don't think the distinction you're drawing between a fee in the abstract and a specific amount is justified or necessitated by how {DIl} has been used in canon.
You can equate the two by saying something like wa''uy' DarSeq 'oH qav'ap'e' "The price is one million darseks" but, as you point out, you still nob the specified amount when you DIl the price (as the idea of the amount agreed upon) or when you DIl the thing you're buying. I expect ghogh'ot "bill" is also something you DIl.
{ghogh'ot}, {rup}, {qav'ap} and even {mab} would be things I expect are typical objects of {DIl}. This is despite the fact that in English, you typically say "pay a bill" or "pay a fine" (not "pay for a bill" or "pay for a fine").
This distinction also appears in English, somewhat differently. With "price" as its object, "give" can mean either "pay" or "propose," depending on context and wording: "I gave him the price he asked." "If you want this car, I'll give you a good price."