How to train for tactics -- counting out , usually wrong ...

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 Hmm, I'm a little confused. You say:

"without having the option of looking at the moves forward, I'm often mis-calculating."

Are you solving the puzzle by using an analysis board (where you can move the pieces)? That will definitely make calculating in your head harder because you're not practicing calculation at all!

For any tactical puzzle (online or in a book) you're supposed to solve it without moving the pieces, use a board only after you've given up. If you still can't solve it by moving pieces, then look at the solution. If you go straight to a board, then yeah, you're going to have trouble doing any of it in your head.

To visualize accurately, go slowly. Only 1 or two half moves at first, and really get a good idea of what that position looks like before moving on. To make it more memorable you can assign each piece a function like "the queen will be attacking that pawn." Consciously review which new squares are attacked or which files were opened.

To count more accurately when there are a string of captures (not always on the same squares) one thing to do is notice who is capturing first. If black captures first and last, then black captures a larger number of pieces. For an even number of captures, one player captures first and the other player captures last. This of course doesn't tell you what the pieces themselves were worth, but this can be a useful shortcut.

For example if your opponent captures a queen on move 1 and you don't capture their queen until move 3 it can be harder to compare the pieces in between. But after you've established the number of captures is equal you can go through the calculation ignoring the queens and focusing on the other pieces.

For example, in the daily puzzle position you linked try to calculate the following moves:

1.Ra1 Bxd2 2.Rxa2 Bxe1 3.dxe5
Black captures first, white captured last, but was this an even exchange?

What about
1.Ra1 Qxa1 2.Rxa1 Bxd2 3.Bxd2
Against black captures first, white captures last, but was this an even exchange?

Hmm, I think I can relate.

When I first began to like chess I only played blitz online. This sort of calculation isn't really sequential so to speak. Sort of like, instead of counting 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 it was 1, 2, 4, 6 10 (not 10 moves ahead, but you know, just sort of going with the flow of a pattern or something... hard to explain). And of course when your opponent does something different on a move you skipped you're screwed heh.

It wasn't until years later when I tried to solve puzzles slowly that I started to calculate carefully and see (maybe imagine is a better word) each individual position during the calculation. This sort of accuracy isn't always necessary, but sometimes it is. It sounds like this sort of skill would help you.

I don't know the best way to develop it, but what I did was, when solving puzzles, I would write down my whole solution before checking the answer. This forced me to go over the moves slowly and in order.

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Yeah, the even odd trick is really nice... wish I had thought of it myself but I didn't.

Hmm, other tricks? Hard to think of any that are similar to that one.

One trick I use when I'm trying to wiggle out of a tactic my opponent's caught me in, is simply to realize I need to make a threat that's bigger than or equal to. So if my queen is under attack that makes it really simple... I have to either threaten their queen or give a check. If I'm about to lose a knight then any threat that's not a pawn will work. Not really calculation, but a way to build a list of candidate moves. It can help you quickly verify whether or not you (or your opponent) is screwed without needing to calculate.

I think you just have to practice it until it becomes more second-nature.  

There are quite a few shortcut-calculations in chess (more in endgames with pawn races) but you can go wrong surprisingly oftne by relying on them and not just calculating it out. 

Especially with tactics - these shortcuts to exchanges are often short-circuited by an intermezzo check or attack on the Q, so it's very risky to just rely on them for multimove exchanges.

Yeah, even if it's something like, e.g., my 5 attackers vs their 3 defenders, I calculate each move because inbetween moves or problems at the end of the sequence can change the outcome. Like hhnngg1 mentions.

But I use the tricks when, for example, maybe I calculated something twice already, but for some reason at the end I keep forgetting the exact position so I'm not sure who is ahead in material.