What about the following justification of the peculiar rules of tsumeshogi?

1. For some games, such as shogi, there exists some relatively common situation in which one player will lose unless they can manage to win without allowing the opponent to play away and win. As the precise means by which the opponent is threatening to win is not important to the urgency of winning before said threat is able to be activated, it is economic to omit the threat and simply stipulate that it exists. This also frees the composer from having to fit this threat into every problem.

2. It is desirable in puzzles to have a unique or nearly unique solution, but higher branching factors tend to make composing such problems increasingly difficult.

3. It is desirable for at least one genre of puzzle for a given abstract to allow the composition of puzzles with very long solutions, to train reading and maintaining a position in one's head, as well as providing a wider canvas for artistic compositions, but higher branching factors tend to make composing such problems increasingly difficult.

Why Tsumeshogi Fulfill these Goals:

1. The most severe threat which still allows a forced win by the opponent in shogi is a brinkmate. The only way to win when brinkmated, disregarding threatmate-removing threatmates, is to tsume the opposing king. So tsumeshogi stipulate that sente's king is in brinkmate, and (usually) simply omit from the board sente's king: the composer and solver no longer need to worry about the nature of the brinkmate: success.

2/3. With the stipulated brinkmate necessitating a forced mate consisting entirely of consecutive checks (aka, a tsume), the branching factor is effectively reduced as only checks need be considered by sente, and only moves which remove the check need be considered by gote. This facilitates the creation of longer unique problems, with the associated benefits mentioned above.

How these Goals could Apply to Arimaa:

1. Disregarding wins by means other than goal, as they are less common, the most severe threat which still allows a forced win by the opponent in Arimaa is a forced goal-in-2. A forced goal-in-1 can only be countered by an immediate goal-in-1, which is rather limited in potential. A forced goal-in-2, however, can be countered by an arbitrarily long series of goal-in-1 threats culminating in a goal.

This is a situation which may be expected between strong players since we already know that strong players are usually able to generate some manner of goal attack, and most goal-in-1 situations at a sufficiently high level will have been preceded by a goal-in-2 situation, so at some point in most high level games, one should expect a goal-in-2 to exist, and for the opponent to nonetheless still have some manner of credible threat regarding which they would desire to have experience making more than simply credible.

So a tsumearimaa would stipulate that gote has a forced goal-in-2, and simply omit from the board the relevant pieces/rabbits: the composer and solver no longer need to worry about the nature of the goal-in-2: success.

2/3. With the stipulated goal-in-2 necessitating a continuous sequence consisting entirely of consecutive goal-in-1 threats, the branching factor is effectively reduced as only goal-in-1 threats need be considered by sente, and only moves which remove the goal-in-1 threat need be considered by gote. This facilitates the creation of longer unique problems which, aside from the benefits mentioned before, can be an artistic endeavor in and of themselves.

A Proposed Ruleset for Tsumearimaa:

0. Unless otherwise specified, the normal rules of Arimaa apply.
1. Sente must win by goal, not elimination or immobilization, in the specified number of turns.
2. Every turn by sente must create a threat to score on the immediately succeeding turn if gote does not move at all.
3. Gote will always delay goal as long as possible.
4. Gote may not voluntarily win by goal: their rabbits may not occupy the first rank at the end of any of their turns. They may still win by elimination or immobilization, though.
5. Neither sente nor gote may recreate a position on the board with the same player to play. This is forbidding 1-fold repetition of situation as opposed to the 3-fold repetition which normal Arimaa forbids.

Why This Implementation?

0. This rule is important to differentiate tsumearimaa from tsumeshogi.
1. This follows from the assumed forced goal-in-2 which gote has: there must be a rabbit and at least one mobile piece (possibly also the rabbit) involved in said forced goal-in-2, which means that any apparent elimination or immobilization by sente, is not actually such.
2. This follows from the assumed forced goal-in-2 which gote has: any turn by sente which does not threaten to score on the immediately succeeding turn, will be answered by gote activating their goal-in-2 threat and winning.
3. This finishes codifying the intuition that "best play" by gote should involve delaying goal as long as possible, and that "best play" by sente should involve scoring as quickly as possible.
4. Without this rule it would be difficult to compose problems with gote rabbits on the first 5 ranks: one turn from goal. Far better to assume that sente has sufficient defense to stop any such attempts and remove the burden from both composer and solver to read that when it is not the focus of this genre of Arimaa puzzle. More freedom in composition means more possibility for artistry.
5. This is a quality of life change which has no effect except to reduce the solution length (but not the complexity or difficulty of solving) of problems which take advantage of the repetition rule. As a puzzle essentially has unlimited take-backs, there is no reason to maintain the 3-fold requirement which gives both players the opportunity to deviate in a normal game.

Concluding Remarks

While I still firmly believe that the more chess-like goal-in-n puzzles which have been most widely disseminated into the Arimaa community have an incredibly important role to fulfill which they do very well, I am interested in exploring whether or not what works for shogi can also work in some small way for Arimaa. An interesting exercise if nothing else.