About busying your Muse... Remember that minds in Eclipse Phase are software, and can be copied as much as you like. If you want your Muse to do two different things at once, then run two instances of it simultaneously on two different devices (say, one in your Mesh Inserts, and one in an Ecto). You could even have multiple AIs, Muses or even Beta Forks, running on different devices in your PAN (one in your Basic Mesh Inserts, one in an Ecto and one each in any number of Ghostrider Modules), and cooperating with eachother or with your Alpha Ego to provide Teamwork bonuses (p.117) on various Mesh-related tasks, including Infosec.

How so? Copying an AI costs nothing. Preparing a Beta Fork (p. 274) costs nothing, and takes only a minute if you're good (or lucky) at Psychosurgery (and can be retried indefinitely if you're not), and once you have that fork, you can copy it as much as you like. Devices to run these minds on are 250 creds each (Ghostrider Module p. 307; and Ecto p. 325). If anything, it's the initial AI that's expensive (unless you're going the Beta Fork route). Once you've paid the 5'000 for a Muse or a Security AI to run on your Mesh Inserts, then spending another thousand on Ghostrider Modules to give it +20 to most tasks is just elementary. On the note of Beta Fork Teamwork... Imagine having a few pre-prepared Beta Forks, skilled in various useful, non-physical skills (Infosec, Programming, Psychosurgery) backed up in storage, and set to instantiate into Ghostrider Modules under specific conditions. I.E. if someone tries to hack your PAN, then four Infosec Betas instantiate immediately, working with a total skill of 90 (p. 274, p. 117; 60 max skill for Beta Forks, +30 for Teamwork) to lock out intruders.

The copy-abuse methods are pretty universal (just look through a few old threads), but Reapers aren't a problem. Just move the story elsewhere. :) It's not a very fun game to be a flying gun, unless the GM specifically makes it so.