I don't expect anyone to do it really but you can modify Sublime if you are feeling brave.
300 pixels is the hardcoded width of the popup. Look for 00 00 00 00 00 C0 72 40 in the binary and replace with your wanted value (for example 00 00 00 00 00 C0 82 40 for 600 pixels).
Here is converter to convert from double to hex - gregstoll.dyndns.org/~gregstoll/floattohex/ (bytes have to be written in reverse in the binary though).
As far as I've checked now, there is only one match in the 32-bit Windows binary but more than one in 64-bit one (first match is the lucky one though).
The width of the popup is not dynamically adjusted to fit suggestions in Sublime so wide popup looks a bit out of place when there are only short suggestions. I guess it would be best if author would make it adjust itself.