I got the dorktronic 3-32K expansion and it did not help. Anyway its a very nice expansion.
Examining what is actually happening, I have this explanation to the problem:
Once the NEOS mouse has been triggered(via the lightpen output) to start sending data, it just sends, sends and continue to hammer the game port. Since it uses joy1,2,3,4 to transmit the change in mouse position, this is hammering the $9120 (Port B I/O register) of the VIA2 chip. The reason is that bit 7 of this register for some reason also picks up joy 3 on game port pin 4. So when the Vic-20 tries to poll the keyboard, it gets interference from gameport pin 4 (joy3) into bit 7 of $9120. That messes up column 7 data which shows up as mistyped keys ("2","4" + some others). For some reason "6" and "8" keys still work, so this theory may not be entirely correct.
The only thing that seems to "prevent" this is when the NEOS mouse is actually moved (e.g. one can type "2" and "4"). It may be that the interfered bit switches from 1 to 0 (or vice versa) by the mouse, which would indicate that bit 7 of $9120 is completely hijacked by the NEOS mouse as long as it is connected.
I haven't found ways to get the NEOS mouse to stop hammering data yet as there is no way to switch it off. I will continue to look for a solution even if it may require some delicate timing relation between reading/triggering the NEOS and reading the keyboard (if possible).
Edit: A quick & dirty solution is to disconnect the wire in the NEOS mouse that is connected to "joy3" (left) pin on the Vic-20 control port. This should remove the keyboard interference without affecting the operation of the mouse (if you trigger it once per screen update). The reason is that joy3 is used for bit3 and bit7 of the communication, but even fast mouse movements seldom go above +7 or -7 in delta x or delta y (7*50=350 pixels/second). For bit7 one can easily copy bit6 as it would only indicate the sign of the delta number. I need to test this to confirm, plus it may not help for the serial port interference in which you may need to remove the mouse or put in a switch (to switch it off when loading or using the keyboard).
I will continue to look for alternate solutions, but as this looks like a hardware problem it will probably require some fiddiling with the mouse itself.
Most interesting I found this on another forum which claims that the first 1351 were in fact NEOS mouses. You can even see the NEOS MB88201 chip inside: http://www.retrocomputacion.com/e107_plugins/forum/forum_viewtopic.php?80555