A.S.Max, I am a life-long Seemiller-style player (40+ years). I can hit a "normal" shakehand style backhand, but not very well. So I can make a few comments on this style of grip. Understand that there are various "modifications" to the Seemiller grip. As nathanso mentioned, you will find examples of those various grips in another thread. I happen to hold my bat with my index finger straight up the back of the bat, pointing in a 1 o'clock position. And each of those will have strengths and weaknesses. So, my remarks will be general in nature.
First, the advantages of this grip...
1) It serves a forehand blocking style game very well, allowing, I feel, great flexibility in touch and direction.
2) The backhand shots are quick and wristy, enabling you to not telegraph where you are aiming your shot until the last second.
3) The backhand shot enables you to quickly and subtly vary the topspin counterdrive with varying degrees of sidespin. In fact, you can swing that backhand stroke (for a right-hander) so far from left to right (picture the bat going around a clock from 9 to 4 o'clock) that you can actually hit a backspin block of a topspun ball. This also can be used to slow a rally down, and put spins on the ball that the opposition is just not used to seeing from "ordinary" players.
4) Because the backhand shot is often executed right in front of your body, you get a direct "line of sight" look at where you are driving the ball, resulting in some very exact placement of those shots.
5) Depending on how you hold it, you can instantly modify your grip and hit a "conventional" backhand. I have Long Pips on my other side, and with the way I hold my bat, I can at any moment hit either a Seemiler backhand with my inverted or a LP drive with a "normal" backhand stroke. This versatility, if you have an "off" rubber on one side, can be very disconcerting to the opponent in mid-rally. This does mean learning a whole new set of strokes, and it takes time, but the payoff is big.
6) Now, here's a potential advantage, but it takes a lot of work...If you have anti or long pips on your other side, you can twiddle your bat and now hit a completely different set of strokes Seemiller style. If you can twiddle mid-rally and do this, it can be VERY effective. I admit, I am still working on this, as it means learning a whole 'nother set of strokes. But I like the results when I get it right.
Now, the disadvantages of the Seemiller style...
1) Lack of flexibility on the forehand. Again, this will vary depending upon your exact grip. The way Dan Seemiller does it, he has NO problem with power or flexibility. And, I feel I don't lack in that area with my grip, either. But some do have this issue.
2) Perhaps the biggest drawback--lack of power on the backhand. Just look at the technique involved, and you will easily see why this is so. I cannot power a backhand past anyone. I can place it exactly and out of someone's reach, but never overpower anyone with it. The way Dan Seemiller holds his bat, with the power of two fingers on each side of the bat instead of only one behind it, he can generate more power than I can (besides the fact that he is light years ahead of me in ability).
3) Lack of flexibility/power to hit balls sent to your extreme backhand. If the opponent angles balls severely to your backhand, that is the Seemiller player's Achilles' heel. You really have to have good footwork to keep that from happening, and when you shift way over to your left to keep that from happening, you expose yourself to a passing shot down your forehand line. Fast, severe-angle serves to your backhand side can be a real issue.
OK, those are the pros and cons that I can think of off the top of my head. There are other Seemiller players on this forum. One I know, and who can give you good advice is a guy named Hookshot.
If I can answer any other questions, A.S. Max, let me know. Good luck in trying out your new style!
Jimweiland