"I've never quite understood the Byzantine idea that a marriage continues forever when Christ said there's no marriage in heaven. Anyone care to elaborate on that for me?"
Very simply because all sacraments/mysteries take place in "kairos" and not only in "chronos". All of them are eternal and participations in eternal life, and marriage is no exception. When marriage is viewed as simply ending at death, it becomes a very exceptional sacrament indeed, for it is then the only one to do so -- it really denigrates marriage, I think, particularly when compared with holy orders, which are seen to be eternal (query -- why? Will we need priests in heaven?).
Christ's point was made in response to a levitical question about remarriage -- an attempt to trip him up. His answer was simply that by asking that kind of question, you are betraying that you have no understanding of what eternal life will be like -- and that these kinds of mundane issues will not be relevant. The Eastern Church has never understood this passage to be a categorical statement that marriage is limited to chronos, and doesn't exist in kairos.
"Why not marry sacramentally the first time and live a pentitential life, to some degree, as an expression of love and gratitude to God?"
Noone is denying that this is the ideal. The issue is -- when the ideal can't be met, then what? Some people are in abusive marriages, some people are in marriages that simply don't work -- leading a "penitential life" in these cases by staying in the marriage is hardly something we want to force on people (and probably something we want to discourage, pastorally). And, in that case, what do we do? Catholics have taken the anullment approach, which is synthetic. Orthodox have traditionally viewed this more realistically -- as a result of sin -- and this is reflected in the penitential character of the second marriage service.
"penance is the suggested deterrent for multiple marriages"
No, that's not the right way to look at it. Penitential character is an acknoledgement that the first marriage broke up due to sin -- it sees the second marriage for what it is -- something that the Church allows in her mercy but which is not the ideal and which itself is taking place because the first marriage was destroyed by sin. It's not a "carrot and stick" approach (ie, "better not get married again, because that means penance"), but rather a reminder of how one got to be where one finds oneself in life.
"So, in most cases, would a better and, in many ways, more penitential option be to attempt to reconcile with the spouse to whom one was and is joined in sacramental marriage?"
Yes, but you're creating a strawman. Everyone agrees that the best course is to try to salvage a marriage that is salvageable. Noone disagrees that this is preferable, where it is possible. So there is no contradiction between that preference, on the one hand, and the actual practices, on the other, for when that is not possible. In the Eastern Church, when that is not possible, the Church deplores the effect of sin on the marriage, but forgives the sinners and in her mercy permits them to be married again. That doesn't denigrate the preference for saving troubled marriages that are salvageable.
Brendan