It seems like this should be wo'vad vISuvqang since there is an object to the fighting
It might seem that way, but the type-5 noun suffixes are usually for marking the purpose of things other than the direct object. The direct object of Suv is usually the thing being fought. A noun with a type-5 is specifically marked as not the direct object, and could be the place the fighting was at (if -Daq), or for whom the fighting is on behalf of (if -vaD).
There's no actual rule that says that direct objects can't be marked with a syntactic suffix, and there are actually situations in which they are. In general, what you say is true, but there are exceptions.
When using the no-object prefixes (like using jI- on Suv here), if the verb is otherwise capable of taking an object, the object is understood to be general, vague, or unspecified. jISuv means I fight in the sense of I fight people or things in general, I fight people or things I'm not going to specify here.
So wo'vaD jISuvqang means I am willing to fight for the Empire in the sense of I am willing to fight people or things in general or unspecified, for the Empire. The wo'vaD is not the object of the verb.
What object are you thinking of? wo'vaD is not the object. The -vaD marks it as the benefactor rather than the object.
It is true that when fighting, there must be someone to fight and that when you state who is being fought, you state them as the object. However, in both English and Klingon it is possible to state the action generally without specifying the object of that action:
wo'vaD vISuvqang "I am willing to fight them for the empire."
wo'vaD jISuvqang "I am willing to fight for the empire."
Without a stated object, both refer to fighting in general and not fighting specific form.