When R' Chanina ben Tradyoin was being burned alive he requested that they remove the wet towels which were prolonging his death. This would show that he was indeed in pain. In addition, when R' Akiva was being tortured to death with iron combs being raked across his skin, his Talmidim asked him how he could concentrate on the Shema. Again this shows that he was in pain. See Gemara Avodah Zarah 18a and the last page of this pdf version of Kinois. Don't both of these show that they do indeed feel pain?
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I would like to suggest that the Maharam is talking about people being thrown in the fire where death is almost instantaneous and is part of the killing. However pain of torture leading up to death is not included in the dying Al Kiddush Hashem (martyrdom) and is therefore painful.
The kina you're referring to was written to mourn for people who died al kiddush Hashem (I don't think we learn halakha or agadah from kinot). The source in A"Z 18a was written, again, to mourn for martyrs who had already died. We can feel bad for the suffering of those who died and talk about their misery.
The Maharam was writing during horrible pogroms in the 1200s Germany. He may have been writing in part to comfort those whose loved ones died al kiddush Hashem and in part to discourage others from effectively committing suicide. I honestly think that the Maharam realized that were martyrdom glorified, he'd lose everyone in the community since the Germans were happy to kill lots of Jews.
It's the same way that we say that suicides can't be buried, but we exclude everyone who's committed suicide assuming they've repented or were sick.