Getting grants at a teaching department while officially being considered an R2 institution
A few thoughts - 

One is that extramural funding is more about gaining prestige from your institution than actually resulting in a net revenue gain to your University.  See this article from the American Association of University Professors website for an explication of the ways in which the focus on extramural funding harms universities.

That said, if your tenure and promotion system is based on securing external funding and/or having time to do research, then you probably still have to play that game even if you know that it's harmful to the university in the long run.  One thing I'm thinking is psychological research about locus of control; if you believe that you are in control of your own success or failure it's been shown that you put more effort into and consequently have better performance than if you believe that others control what happens to you and that what you do doesn't matter.  It does sound like the system is rigged against folks in your situation, but nonetheless, you can still do your best to put together a competitive application - have folks read over your applications, look at other people's successful applications, etc.  Perhaps there's an office or staffperson on campus that helps with applications for external funding that could be a resource?

Finally, it sounds like there are some more systemic issues about courseloads and advising loads being too high.  These seem like great things to raise during faculty union meetings or to bring up to your Academic Senate representatives - you're probably not the only one feeling this way, and if you can open up a conversation with other faculty maybe there are some changes that can be made in the way things work.  Here's a case study about how faculty unions dealt with this in Ohio that might offer some inspiration for taking collective action.