Here's a thought.  You could have Akane come in, stare at the stranger, 
ask "Ranma is that you?"  When he admits it, she could come on in and 
say, "You don't mind sharing the bath do you?" or something like that.  
After, he's a member of the tribe and they don't have a taboo against 
opposite sexes bathing, since their gender switching makes it 
impractical.  The result being Ranma comes tearing out of the bathroom 
instead of Akane.  

As far the sparring match goes, you've changed the wrong part in my 
opinion.  The important part of the original scene in terms of setting 
the groundwork for their affection was the part where Akane's nice to 
Ranma, defending "her" from Nabiki's rudeness and offering him 
friendship.   

Of course, the engagement does have one thing going for it.  Surely this 
Genma would never have trained Ranma to be a "man among men".  Any 
homophobia he picked up had to be from his peers.