I feel like I must be missing something obvious, but as far as I can tell this level is impossible to clear. The Borg drones quickly adapt to both hand phaser firing modes and the phaser rifles normal mode, so I was only able to kill them using the phaser rifles alternate firing mode... but it doesn't have enough ammo to rely on entirely. And then there's that big fanfic gun designed specifically to get around the Borg's adaptive shields... that is disabled.

So: what am I doing wrong?

The Borg adapt quickly but you cam bring them down, the phaser at low level can stop them after a time, it is a developer error but it works. try to move to the objective and the level doors if need be.
The first mission on the Borg ship is big, detailed and beatable. do not use ammo so much.
but when they adapt, try to get to the distribution nodes. the big bad Borg drone at the end is fairly easy, simply move to the forcefield towers, use the tricorder and blast the panel then the drone using the imod, repeat till mission ends.

The imod is a cope-out for players but it works,

You are suppose to not really attack them unless you need to, they will ignore you until they don't.
And you can destroy Distribution Nodes which will disable the Borg.

You will eventually disable the jamming field, but you have to find a particular disnode to do it. you will have to use skill and tactics mentioned above.

While the Borg adapt to your weapons, they don't adapt to Telsia's/Chell's - if you get into a fight and you are not on your own, you can pull back and let them do the heavy hitting.

If it's during one of the parts where you are fighting by yourself, try to run past/around them if possible, otherwise the Compression Rifle can damage them if you shoot near their feet (the 'area effect' damage isn't adaptable). It does take the secondary fire mode/a decent amount of ammo, but it can get you over the hurdle until the I-Mod is able to be used again