You get a certain amount of gold/seeds per step and per node you hit, you can see the numbers for some of the maps in the HBC wiki even.

If you want to try to research whether speed affects it or not you should really pick a map without any random tiles and have different speed teams go through it, like the early area 1 maps. Maps like the 80 stamina gardens are just way too unreliable.

well just managed to get spinning around the 25 stam gold for this

got 3175 golds for 2 times in which i succeed in passing all node and reaching the point where walking no longer gives you gold

so yeah there might be hard limit each map or maybe it's just my luck

While I agree a flat map with no random tiles would have been optimal, you'd also only have one data set to compare to another (slow vs fast at distance X) and would never have any (slow vs fast at distance Y) for comparison. Another problem with doing the test one something that level is the level size is so small the numbers on the received items would be smaller, which makes it harder to determine whether there the results is just the RNG of what you've received from a unit's move.

That being said I did some tests on 1-3 mostly to just watch a single units' gains. Watching a 444 speed unit I had numbers ranging from 29-46(coins). Then with a unit with a speed of 239. I saw numbers ranging between 11-26. Given these sample sizes are not huge maybe about 50 (moves) per unit and some of those moves resulted in seeds. So take this as you will.

It certainly seems the random amount you get does use speed / distance as a metric in its generation. Something like { (Distance * RNG) * Difficulty multipliers }. If anything this means that taking full set of slow units with the goal of having more turns isn't going to INCREASE your end rewards, if anything it would only bring your ending rewards to tighter cluster for finding out the average rewards for a given map.

(Just for fun) It can actually have the exact opposite effect. It can cause you to lose seeds, (but not really gold) if you use a slow enough unit on a low enough level. There were more than a few times my 239 speed unit would make moves and get nothing, my guess is that the move - reward being chosen was a seed and { (Distance * RNG) * Difficulty multipliers } < (.5 or 1) -I can't reasonably discern which of those two values it is. And therefor rounded to 0.