Feed back requested for a simple abstract wargame

I've been noodling with a simple game that will be made using 'rustic' counters, needs to play pretty quickly but have some tactical play. Hopefully by having to pick your next piece to play without knowing what your opponent will do will give the tactical part, I've been thinking on a way to have to choose next two pieces whilst keeping it simple as one in the hand

Rules:

Draft your army
Fill a 5x5 grid with 'tetris' style blocks totalling no more than 4 and no more than 3 in any dimension (e.g. 2x2, T shape, L shape, 1x1, 1x3).

Deployment
On the 6x6 battle board place three pieces down so they do not overlap or go past the second row. Pick the first piece you will play next and hold it in a closed hand or under a cup or some such

Following turns:
show piece to opponent and you can either
lay it so it touches one of your pieces already in play as long as it does not overlap any other piece (yours or opponents)
Put it behind your first row and move it and all the pieces it touches forward one row, this will push any opponent pieces back one row as well. If a piece has more than one depth the remainder is left off the back of the board.
Odd shaped pieces could make use of gaps and still push pieces forward (L and T shapes mainly here).
Once you have a column from your base line to the opponents baseline then the opponent can no longer lay pieces in that column
Pick your piece for your next round.

Victory conditions:
Control of any two touching columns, one must be from central pair
Control of any two columns but these must be on both left and right flanks and neither of the central columns.
If both sides run out of pieces count up the area of pieces removed and add 5 for control of a column.