I say this as someone who would always rather use his own kit for all of the reasons you gave. Your motives are pure. But it's not your gig.
As the opening drummer, insistence would be bad form. Ask, by all means, but be prepared for disappointment. From what you wrote, it sounds as if you already received your answer.
Now depending on the following unanswered questions, there may be some partial solutions.
Are you opening at the request of the party host or the headlining band? If the former, perhaps you can press your case with the host. If you try again with the headlining band, first follow Mitch's advice and offer your kit for the evening (but the headlining drummer may feel the same way about his kit as you do about yours).
What is the stage like? There may be logistical reasons for denying your request beyond the time required for a changeover: The stage may not be easily accessible and/or moving your equipment might be disruptive to the party. The stage may simply not be large enough for two drum kits, and why should the headlining drummer have to do a quick setup after you're finished, especially if there's a sound person (and even more so if the headliner is paying for that)?
Are your bandmates using the other band's back line? If so, you don't have much of a case.
Even if you "man up" (which is my suggestion), you should still be able to use your own snare drum, bass pedal, and select cymbals (ride and hats—bring your clutch). You should also be able to make minor adjustments to the supplied kit, subject to standard etiquette that has been covered elsewhere on this forum.
If it's really that big of a deal, perhaps your band should seek another gig for its only show of the year. I don't know anything about this gig, but my guess it that the advantages outweigh the disadvantages and that it could result in further opportunities for your band if you play your cards right. Don't blow it: Be a pro, go up there and do the best possible job that you can.
Sorry for being a hard case. I'm sympathetic to your cause, but you're not really in a position to make demands. No matter who invited you to play this gig, why give them any reason to regret that decision?
Worst case: Chalk it up to experience.
Al