I've had similar challenges, both with getting group buy-in to try new systems and with getting people to feel comfortable GMing anything at all.
My solution was a long-game process of changing the "landscape" of how people at the table viewed their role in the game. I didn't set out to deliberately address the challenges you're facing, but it's accomplishing your goals. Here's what I did, but please keep in mind that it was a lot more organic and unplanned than I'm going to make it sound. What I'm describing was a haphazard evolution over about four years.
I've been engaged in a long, slow process of crafting the gaming environment so people feel more empowered to influence the game as players. This means asking them for more input and giving them jobs traditionally left to the GM. We were playing D&D 4e, a game with a great deal of fiddly bits, and I needed to pass off as much of the burden as I could: from designing NPCs and choosing plot points to tracking initiative and debuffs in combat.
As a side effect this demystified the GM's role because I opened it up for analysis and participation, so when the time came the leap to GM was less daunting for my friends. They knew what it entailed and they'd seen me get help with it from the group so they knew they wouldn't be on their own.
In addition to giving players more agency in campaign design and making the GMing process more transparent, I groomed one particular friend (who was already more proficient with 4e mechanics than I) and accompanied him in preparing a short game in the existing system which he ran on nights I was too burned out to run things myself. By focusing on one person who I knew possessed ready potential and was game to try it, I had practical lines of action beyond begging folks to GM sometimes. When he was ready and he ran his game, it was fun! He made mistakes and we didn't care. There were glorious TPKs. This further clarified that GMing is not an elite or perfectionist role, and that I was not guarding it jealously: it's just another role you can inhabit as someone who plays RPGs.
Then (and at this point we'd switched systems to Fate, which is much less prep-heavy) I invited others to run single sessions of our main campaign. It was low pressure because they already knew the system and the setting, and I'd been engaging them in the story-design process for some time.
(As a side note: we switched to Fate at the end of a two-year campaign in 4e. We felt like we'd basically "done" 4e, and the transition was smoothed by using the Dresden Files RPG. We'd all been reading the Dresden Files novels, so enthusiasm was high enough to overcome trepidation about a radically new system.)
Roughly simultaneously I started running one-shots of simpler systems when we didn't have all our participants for the main game. That let me introduce them to new systems without sacrificing main-game time to do it, so they felt less resentful of the change. When I couldn't be there one evening, I gave them Everyone Is John to run amongst themselves. They said they like horror, so I introduced Cthulhu Dark.
Not everything we tried (like My Life With Master) was a big hit, but it always expands our vision of what gaming can encompass--and over time made us more open to jumping between systems depending on what we felt like each week. We learned that it's okay to try stuff we aren't sure we'll love: sometimes we love it, but if we don't... well, we still had a night of gaming with friends.
Recently we've reached the point where people volunteer to run sessions of the main campaign (right now we're using the Atomic Robo rules for Fate), and they ask for help to run a one-shot in a system they really liked (especially Roll For Shoes and Cthulhu Dark). A couple folks have stepped up with systems or campaigns they want to try out and offered to run them for us (we've got Paranoia and a zombie apocalypse game waiting in the wings). As of last month every person in the group has run at least one session of a game. Our group feels more like a group of friends who play RPGs, than like a GM who runs players through his games. That's the change you need to be looking to make.