Not sure on what wheels you need for ride tires.
Everyone I know who has used ride tires suffers from understeer. If you want more steering and overall more grip then Shimizu 571 fronts and 572/575 rears depending on temperature.
Tamiya tires only work on hot summer days to my knowledge.
If you want to stick to the rides then obviously change what you have before you buy new tires. I think the heavy weight pivot post is a bit of a waste so scrap that first off. If you find that takes away too much rear grip then go a soft rear spring with minimal pre-load. Should make up what you lost. The center screw in the t-bar would also assist in making up for lost rear grip from the pivot post.
The softer front spring will give you more front grip so that would be the next thing to work on if you still have understeer.
Another thing to look at is your ride height front/rear. Lifting the rear will give you more front grip as well.
Also do check the steering travel. You want the uprights to almost touch that plastic post on the bottom front arms.
Finally toe out is a big thing as well. This may or may not work with the rides but definitely works with the shimizu rubber. You want to be looking at 3-5 degrees toe out either side.
Actually did have one more suggestion. You could also consider moving the battery forward a few mm at a time. This should also improve front grip.
Just change one thing every race. See what happens and go from there.
I don't think I've left my car the same for a single race yet from the start of the year and we race weekly. Theres always something to experiment with and see how it behaves.