In no particular order:
Set up some combos instead of just taking the first matches that you see. You should be able to see 2 or 3 chains into a combo before it starts. In the beginning there it just seemed like you were hitting 1 or 2 chains instead of taking the time to arrange the board for the shot you wanted. You should be stacking up coins next to one central point where most of the action will take place during a combo when the board is moving slowly and only start the combo when you're ready. I tend to do things so that I can just do a repetitive motion throughout the combo, like left, pick up coins, right, drop coins. That way you can stack up a chain reaction quickly and then go find some more matches while the 2 or 3 combos you stacked up go off automatically.
Make more 2 coin matches. 1, 10, and 100 denomination matches are harder to make since you need 5 coins to get the chain going, but they take just as long to disappear as 2 coin matches. If you could just start putting 5s and 50s together you could buy time to get over to the next stack of 5 coin matches and extend a combo that way. Also using a rank up on 1s, 10s, and/or 100s makes it a lot easier to extend the combos.
I could hear your stick hitting the sides of the hole which means you're wasting motion when you dash sideways (something I still have to work on, but I don't think it's as big a problem with sanwa sticks and their low resistance). There's almost no recovery on dashing sideways, so most delay is coming from you or your stick.
Don't stop to watch your combos. You're stationary after you've released your coins when you should be dashing off to start another combo in the chain.
On a related note, stop thinking at the apparent speed of the game. You can move much faster than you are moving... Honestly , I find the best practice for exchanger to be playing magical drop 2. Its a much faster game with similar mechanics and more pieces on the board. While the window for comboing on exchanger is smaller and less forgiving, the speed of your character and the fact that you can lower the board mid combo add up to exchanger being easier to play, in my opinion. I try to beat the MD2 on level 8 with the fool in vs mode and once I can do that fairly regularly I play exchanger. After getting warmed up exchanger seems so much simpler on it's level 8.
Remember that the coin that appears as a result of a match appears in the place of the coin furthest to the bottom of the screen and, in the event of a tie, to the rightmost coin. You can't wait for the coin to appear to start thinking about your next move, so you need to account for that while you're planning your combo.
I'll update the post if I think of anything else...been a while since I've played.
