I would rather wait for progress. But I don't know how skilled are you. So in my opinion the best is to go and run any variant and start fight with first opponent. If you go well it mean yes you got chance to go with your roster.
Probably not; variants were designed for summoners with a bunch of r4 5*s. They are doable with 5/50s, but only if you’re skilled, and it does take awhile. Also, it doesn’t look like you have the champs you’ll need for any of the variants.
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So in my opinion the best is to go and run any variant and start fight with first opponent. If you go well it mean yes you got chance to go with your roster.