Going against the general consensus of members I would not rule out shallow water. Far from it. I have been fortunate to catch a large number of river tench, some of a very nice size of 5 lb +, all from very shallow waters of no more than 2 1/2 ft. These captures have mostly been on hot, sunny days and mostly early into the start of a new British river season (Mid to late June). The fish are likely attracted to the swim in question because the shallow water heats up very quickly. Dip your hand into this water and it feels so much warmer than the deeper part of the main river.
Agreeing more with fellow members the swim I fish for river tench is also very slow. The swim is a still area connected to the river via a relatively small inlet. There is a flow or drift, but it isn't like that of a river. It's slower, sometimes it goes inwards of the pool and sometimes out and changes direction frequently. It's an unusual spot, but very productive.
I have written about some of my river tench captures in the following threads on the TFF:
viewtopic.php?f=77&t=13506
viewtopic.php?f=337&t=18080
viewtopic.php?f=337&t=21612
River tench are not all that common and are more classically considered a species of still waters. If you want to catch your first you may have a better chance in a still water. If you want the challenge of a river tench why not ask around for advice from fellow anglers and in tackle shops. Good luck!