vanguardviper

Quite true in general. However, in this case, it's fanciful to expect to get 200 A through the thin leads on these TO-220 devices. So yes, a 180 A part should be OK. It should be rated for at least 80 V; 100 V will give better margins.

Sorry I did not answer the question. I belief it is not good practise to downgrade component conducting high current like FETs. 
Just my 2c.

Switching from grid to battery is a signal from control to Relay ... If we assume the relay is working fine, then we check load.
you said Load is 500 to 1 Kw .. that shouldn't make that problem for a 10KW inverter ..
so I advise:
- check grid status (Voltage, Frequency) if the grid voltage is lower than normal that could cause that delay (solution is a good regulator)
- check Cables, if cables diameter is not well calculated or the length between inverter and load is big, that will cause drop voltage which get us back to first case.
- check inverter settings, especially the response time (usually there are two options, one for appliance (20ms) and one for sensitive devices like PCs (lower than 10ms)
- check battery condition, and concentrate on terminal connections, also check connections on circuit breakers if there is any.
- If your system is NOT a common Neutral (combined grid Neutral with inverter output Neutral) that could cause such a problem (thou I don't recommend that kind of install)
 
I advise you to use a small UPS for sensitive devices (routers, PCs .. etc.)
Actually, I've done this with my own system because I have the same problem you have, SPECIFICLY when gaming on my PC
 
hope that help ...