Just something quick I notice. Both you and your training partner are doing many things well. But I notice your recoil time, both of you, needs some work. Meelis's stroke is a little too long and even though he is very consistent in getting that first forehand in, if it comes back he is reacting from a compromised position because he is not setting for the next ball until after it is coming back. You get set a little quicker than he does but it is still a little to late and his late reactions seem to be a little faster than yours. This might also be because, when you give him his forehand shot back, your placement is consistent and predictable (good for the drill) so even though he is not ready when the ball is coming back, he knows where it is going. When he is giving you the ball back after your first forehand, neither of you really know where the ball is going and it never goes to the same place twice.
But, the issue for both of you starts with the fact that your recoil is way too slow. This makes it really hard to have good footwork and so you are both taking a lot of balls from out of position. Meelis is not starting to get ready until the ball is almost at the net coming back. You are not ready until after Meelis makes contact and the ball is already coming back to you. For both of you, it affects your forehand more than your backhand because the forehand is a bigger swing but for both of you the stroke on the backhand is very long and the recoil is still pretty late.
You need to work on getting back to a set position way earlier. Ideally you should be set as your shot is hitting the table on your opponent's side, so you can watch the contact of the opponent's racket with the ball and see where they are going before the ball is coming back to you (as they make contact, not before they make contact, before they make contact you can be fooled). You guys are close to the table on those first strokes. If the strokes are shorter and your recoil makes you ready as your ball bounces on your opponent's side, then you will be able to watch for where the ball is going.
For both of you, your arm is stuck at the follow-through position until you realize that the ball is coming back. And then you try and move very fast to where you think the ball will go but it is already too late. Part of the success Meelis has after you return his forehand shot has to do with the fact that you put it where you want. When you are the server and Meelis is putting your first forehand shot back, sometimes it is deep to the forehand, sometimes it is in the middle, sometimes it is at your backhand. So there are times were you are moving towards the forehand side and the ball hits you in the body. If you were set before he hit the ball you would see where it was going rather than trying to guess and hope it goes where it should.
Try two similar drills with a random element.
With the first drill, keep the serve, the first push and the first attack from the backhand the same and then make the the blocker's return of the backhand attack random so it can be anywhere on the table and the server's job is to see where it is going and move to it with the forehand (even if the return is deep to the backhand side). To get that forehand when you don't know where the ball will go until it is hit, you must get yourself back into a set position before your opponent makes his return.
With the second drill, try the same drill you are doing up to the first forehand topspin, then, have the return after the first forehand topspin be random, so it can be anywhere on the table. Then play that point out as you would a regular point in a match. If the ball could be going anywhere on the table, to be able to field the return after the first forehand topspin, you have to be set before the ball reaches your opponent's racket so you can see where he hits it, watching the racket angle, the stroke and the contact of the ball.
Both of you have very decent strokes and are doing many things well. Shortening those strokes and speeding up your recoil will help the two of you considerably. When you are farther from the table a longer stroke is okay. But close to the table, you need to get ready much faster.