It feels like my reflexes are a good bit slower.
Any idea how I can simulate that environment and practice those skills or maybe just solve the problem another way
Some people want to belong to a group. Some need the group to get something done. Some want to control how a group thinks etc etc. And the path you take will be different in each case. So think about what need of yours you are trying to meet.
In general they will pay attention to you if you show you have some value to them. Simplest way is to just show them you are paying attention to their views. Reflect it back. "so what you saying is...". Do it in a genuine non judgemental way. If its a formal meetings send out email summarizing the discussion acknowledging all sides and issues.
Just come into the group with your preconceived agenda, and ignore what everyone else is saying.
You should have something to say. That always helps.
Once you have ground, you don't have to talk fast. Talk normally and your listeners will adapt to your speed. You can control the speed of conversation just by slowing it down yourself.
People who like to talk and can do so quickly? I can't say I've met many who like to listen, so maybe listening as a strategy would be the better bet for this group.
They might be jumping in faster because their level of familiarity is strong already.
It's not so much the speed of talking that is a challenge as that the rest of the group are much quicker to respond or jump in when there is a pause.
Consequently Its very hard to say what I want to say.