I'm reading the rules and I see -
1st "game deadlines" - 1 game per week - we can manage that!
2nd - a stalemate is when both opponents don't want to engage in battle on the opponent's terms (removed from the rules)
and 3rd the most important thing is we want to engage in battle (no longer related to point 2) let's say a little later - it's fun to strategize!!!!!!!
there's nothing about this in the rules - draw your own conclusions

PS - I'm saying this again, there isn't such a situation yet, just explain what the problems are.