Maybe in any case Abaye could not have said that the problem with a holiday lamp is the burning of sacred items, since we are talking about a lamp lit on the eve of the holiday. Therefore he had to say that they decreed regarding a holiday lamp because of a Sabbath lamp.

As for a lamp lit on the holiday itself, he too would agree that it is forbidden because of burning sacred items.

In the conclusion, the lamp is lit on the holiday itself in honor of the Sabbath.
Beyond that, you’ve raised an interesting question. Does lighting the lamp on the eve of the holiday count as burning sacred items on the holiday? The Nimukei Yosef in Bava Kamma, as is well known, connects lamp-lighting to the question whether one’s fire is considered like one’s arrows, and wonders how it is permitted to light Sabbath candles, since at every moment I am considered to be lighting the fire. He distinguishes between Sabbath candles and tort law, and the question is which side to classify the burning of impure terumah oil under. But this is not the place to go into it.

What I meant to ask is this:

Rabbah’s view says that there is no problem at all with burning sacred items on a Jewish holiday, and the whole reason it is forbidden to light candles with burning oil on a holiday is a decree concerning a holiday because of the Sabbath; and on the Sabbath it is forbidden lest he tilt, since he is anxious to complete the commandment of burning sacred items.

Rav Chisda’s view (which is the one accepted in Jewish law) says that there is no problem lighting Sabbath candles with burning oil, and the whole reason they forbade it in the Mishnah is because it is talking about a Sabbath after a Jewish holiday, and on the holiday it is forbidden because sacred items may not be burned on a holiday. Meaning, on an ordinary Sabbath (not after a holiday) there is no problem lighting with burning oil.

I am suggesting a third approach that combines the two (Rabbah and Rav Chisda): on the one hand, it is forbidden to light Sabbath candles on an ordinary Sabbath with burning oil because there is a concern lest he tilt, since he is anxious to finish his commandment to burn sacred items (that part I took from Rabbah); and on the other hand there is also a problem burning sacred items on a Jewish holiday (like Rav Chisda), and therefore on a holiday too it is forbidden to light candles with burning oil.

The advantage of this approach is that it lets us give up Rav Chisda’s forced interpretive setup in explaining the Mishnah in “With What May One Light,” namely that it is talking about a Sabbath after a holiday. The practical halakhic difference would be that it would be forbidden to light candles with burning oil even on an ordinary Sabbath. And this also fits the baraita they brought in support of Rav Chisda:
It was taught in accordance with Rav Chisda: All those materials with which they said one may not light on the Sabbath — one may light with them on a Jewish holiday, except for burning oil, because sacred items may not be burned on a Jewish holiday.

You’re ignoring their underlying positions. Perhaps Rav Chisda held that we are not concerned about “lest he tilt” regardless of the Mishnah, and therefore he cannot explain it that way. You yourself can of course suggest such an explanation, but there is no difficulty on Rav Chisda.

There are two difficulties with Rav Chisda. One was already raised by Tosafot: from the supporting source they brought for him, it sounds like it is forbidden to light with burning oil even on an ordinary Sabbath (not after a holiday). Another difficulty is from the Mishnah, which lists the oils with which one may not light on an ordinary Sabbath, and within that list mentions burning oil without noting any exception; and Rav Chisda gives a very strange interpretive setup of a Sabbath after a holiday (just for burning oil). So I don’t understand why it wouldn’t be preferable simply to answer as I suggested above, and then all the difficulties are resolved smoothly.

As I wrote, you are seemingly right. Apparently Rav Chisda did not hold that way independently of the Mishnah, and therefore was not willing to interpret the Mishnah that way. By the way, a similar interpretive setup appears at the beginning of Beitzah (2b) regarding an egg laid on a holiday, where they explained it as referring to a holiday after the Sabbath.

A theoretical question:
Can a halakhic decisor who accepts the authority of the Talmud rule in accordance with my suggestion above? Or is he obligated to rule only like Rav Chisda (as the medieval authorities ruled)? Or perhaps he may choose only between Rabbah and Rav Chisda, but not combine the two?

There are examples of halakhic rulings that combine amoraic or tannaitic opinions in a way that matches neither one. I once brought an example of this from the tannaitic dispute in Ketubot, where an amora rules neither like the first tanna nor like Rabban Gamliel regarding migo in a claim of virginity. See column 257.

Is it permitted to burn sacred items on the Sabbath, and specifically only on a Jewish holiday is it forbidden?

The opposite. On the Sabbath it is forbidden, and on a holiday they discuss whether it is also forbidden.