MsDoe said: Welcome to the Forum!
First, I would not put the plant in water, that will just slow it down.
If the bottom part of the pot stays mushy soggy wet for any length of time, the plant will not send roots deep in the pot.
Also, if you water very sparingly, and never wet the bottom soil, the plant will not send roots into the very dry bottom of the pot.
So, to strike a balance, you have to have the proper pot and the proper potting mix.
The pot should have lots of drainage holes in the bottom. If it only has one, drill some extras.
The potting mix should be a fast-draining succulent mix, with 30 to 50% additional grit mixed in. Grit can be pumice, gravel, or chipped granite poultry grit. If you use perlite, rinse thoroughly or the fine dust will plug up the air spaces.
With this combination, when you water you can soak the whole pot, top to bottom, but the lower part of the pot will not stay soggy.
Let it dry out before watering again.
Think about the roots--they need water but they also need air, and they will rot if they stay too wet. Manage the plant for healthy roots and the top part will look great.
A pot that is too big also makes it difficult to manage drainage properly. The middle tends to stay too wet. I don't think I'd go for a bigger pot until you have healthy root growth. And don't keep digging it up to check the roots! You'll know when the top growth improves and new side growth appears.
I don't think a plastic pot will keep a healthy snake plant from sending out new rhizomes.