My inclination would be to put the probes in the centre of the cavity, and you will need only a very small insertion for bandwidth of the order of 1%. At least then you are coupling primarily to the intended mode in the waveguide, rather than higher modes which may produce unexpected results and add extra reactance.
It is advisable to maintain symmetry as much as possible. If the input and output couplings are the same and the two irises are the same and the three resonators are tuned, the filter has to work at the centre frequency, doesn't it. The bandwidth and the ripple may not be quite what you wanted, but you know the irises are right, being from a proven design, so you have only one thing to adjust, in/out coupling.
I made a dual mode cavity for 5.7GHz (with N connectors) The probes were 6mm diameter by 3mm insertion and bandwidth about 1%. That was square waveguide, yours will be rectangular, no doubt, and my intuition says that will increase the coupling somewhat. I would be tempted to start with something 3mm diameter and close to flush with the w/g wall. Easy to reduce the coupling with a shim under the connector flange.
73 es gl.