Since the OP doesn't mind that the topic drifted towards a palm muting debate, I will add my $.02. I have played a lot of Reggae and seen a whole lot of live shows, and the only people I have seen use palm muting on Reggae are younger/non-jamaican guys. I am aware of Robbie using some palm muting, but he is the only Jamaican bass player I am aware of who uses the technique.
I like to get a good Reggae tone on my Jazz bass by turning the bridge pickup all of the way down, and the neck pickup a little bit down, which seems to mellow out the sound and a give a softer attack. Then I turn the volume on the amp way up, and play with my right hand on the neck with a very soft touch.
I learned this by watching videos of Family Man play, and years of experimentation. I will make EQ adjustments on the amp, such as cutting out some mids, but I find the finger technique to be the most important. I have gotten lots of compliments on my tone when playing like this, especially from other bass players.
Oh, and I can't forget my secret weapon - flatwound strings. For a more modern Reggae tone roundwounds are great, but if you want an old-school roots Reggae tone I feel that flatwounds are a must.
I have heard palm muting used by a lot of the Hawaiian Reggae bands, and I just don't feel that it has an authentic Reggae tone. It seems they are trying to cover up for the fact that they are using roundwound strings and have a bright, trebbly sound. However, for newer R&B, ala D'Angelo, and feel that palm muting is a great technique.
I think as long as you pay close attention to your technique you should be able to get a good tone out of any amp that puts out a decent amount of power.