Suggestion of TT blade and rubber

Hello all, I am new to this forum and this is my first post here. I have been playing TT for close to last 2 years, both in office and club. I also got training on weekends from a local coach for a few months. I started with a premade bat (GKI Kungfu DX) which is very decent for beginners to learn strokes and spin. I have so far developed very good forehand topspin, smash, block and push, but my backhand is still not aggressive. I rely more on drives, push, block and sometimes punch blocks on my BH (cannot loop or topspin).

Last year I assembled my first custom bat, with Tibhar Carbon Shot blade, Donic Coppa JO Gold rubber on forehand and Friendship 729-08 rubber on backhand. However, the setup seemed to be too fast and lacking control for my skill level, not to mention it is quite heavy too. The dwell time seems to be very less, particularly on the FH side and due to this, pushes often goes long or out of table and in general lot of shots tend to miss the table unless I can control them well. Lifting heavy backspin balls with slow spinny topspin is also difficult. Though I must say the shots are much more powerful, speedy and difficult to return when they land on tables.

Anyway, frustrated with the lack of control in my custom bat, I went back to my premade bat while obviously sacrificing the speed and power. Now I am again looking forward to take my game to the next level and want to try out a faster bat with good control.

1) Can someone tell me which one is the reason for lack of control in my existing custom bat - is it the carbon blade (Tibhar Carbon Shot) or the fast rubber (Donic Coppa JO Gold)? Or is it both?
2) I was wondering if I should go for a totally new combination of custom bat which provides good control and decent speed (e.g. Allround wooden blade and Mark V rubbers) or should I keep the existing carbon blade and replace the rubbers with slower rubber or may be keep existing rubbers and replace the carbon blade with slower one-ply wooden blade? I am totally confused which option will give the best of both worlds (speed and control).
3) I recently played with a friend's custom bat with Joola Carbon blade with Mark V Max rubbers on both sides. Mind that it is not a carbon blade per se, but basically a one ply wooden blade with carbon coating (or something of that sort). My forehand topspins and smashes were amazing with this bat, but pushes were again going long and it a bit faster for my backhand. Will it be a wise choice if I switch to this blade with a lower thickness Mark V (1.8-2 mm on FH and 1.5-1.8 on BH) to gain the desired control and speed?
4) Given my BH style with no looping, do you think I should consider short pimples or antispin rubber? I have no experience with either of them. Or should I just use a controlled inverted rubber of lower thickness on the BH?

Your valuable inputs will be much appreciated. Sorry for the long message.

Thank you very much for your suggestions. So between the below two options which one do you think will give me more control on my forehand side?
Allround wooden blade with Donic Coppa JO Gold on FH
Tibhar Carbon Shot blade with Mark V 1.8/2.0 on FH