Hmmm, I did something similar a while back. The proprietary softphones were poor so we ended up using free softphones coupled to the PBX via a free softswitch... this allowed us to script into each CRM.
The beauty of this approach was:
1. Absolutely free and no licensing worries
2. Tight blended integration with clients CRMs even those not considered possible under the commercial solution (ick)
3. Client screen-pops on inbound and blended
4. Fully self-documenting call flow with dispositioning on hangup
5. better management instrumentation than the commercial PBX allowed
How to best accomplish what you're after would depend on the CRMs, the PBX and your license restrictions (if your PBX is commercial) but usually can be solved without additional costs.
Truthfully, the softphone shouldn't be an issue at all. There's nothing you can do on a softhone+PC that you can't do on any hard phone+PC. It really isn't difficult to make the agents PC aware of the telecoms or to tie in screen-pops, Dispositioning and active CRM.
You say you don't want a dialler but a free progressive dialler (as opposed to predictive) would be easy to justify regardless of how many agents you have. Actually, if your numbers are coming through excel or web then one of two solutions (macro/greasemonkey) can mean you have free click-to-call for your agents even WITHOUT a central dialler.
Like I said, what options you have depends very much on the specific circumstances, but I'll stand kicking if there isn't a free solution to tie everything in over multiple client campaigns and multiple CRMs.
I'd give you my contact details but I'd get accused of advertising again so, unfortunately, all I can do is advise you to talk to your IT guy/girl about how free solutions (macros, greasemonkey, softswitches and free sip clients) can be leveraged to provide what you need in terms of CRM/Call integration.
or... call your PBX vendor and get bent over.