Maybe the mall has already made a deal with a merchant, and it's a lost cause.
Any way, talking to mall management (together with hockey club managers, if there are any) early makes sense, to see whether there is any hope at all. Do they now that an oval rink might lose both figure skating and hockey communities?
From everything I've heard, running a rink is a big job, that requires a fair degree of expertise. So I guess offering to take over rink management is probably out, if you've only a few coaches. Do you have an active figure skating club? (Of course, very few clubs have successfully run rinks.)
If you've had skaters go to Nationals, they might come for free to help save the club.
Maybe it is a good opportunity for one of the other rink managers to add a full sized rink, nearby. Might be worth talking to them too. Especially if you can interest community leaders in the idea of subsidizing a rink, and you can virtually guarantee them some rentals from the figure skating and hockey clubs.
When I tried to look into circumstances surrounding the potential closure of some nearby community-run rinks, I found myself completely amazed at how much money communities pump into recreational facilities. Not just ice rinks - parks, playing fields, basketball courts, pools, tennis courts, other sporting facilities, arts centers, community centers. Apparently they figure that these things help attract people to the community, and prevent some kids from joining gangs for lack of anything else to do, and they often have annual parks and recreation budgets in the millions or tens of millions of dollars. It seems self-serving to politic to get some of that money for your activity, but that really is the way the game is expected to be played.