Obviously a dual-SIM phone can alleviate this problem, as can a modern phone with multiple SIP accounts configured, assuming then you have a good data plan, or can live happily as a simple hotspot-whore, (and most people could!).
To cite a reference, these Nokia phones have SIP support within the OS, so battery life is excellent, compared to having to run an App just for SIP accounts, (like SIPdroid).
http://developer.nokia.com/com...
The Nokia N9 and N900 phones also have SIP support within the OS and battery life is very good. Hmmm, I never bothered to look, but what about Jolla's Sailfish? For that matter, does anyone else know of another low-energy SIP stack in-use? I don't think iOS offers it, but I've been wrong before.
As to how to get your company telephone line (DID) in a workable state so you can access it via SIP, well, you're on your own slashdotters. (Hint: lowest common denominator is something like an OBi110 PSTN FXO adapter). In fact an OBi110 and a Raspberry Pi runny asterisk/FreePBX can forward incoming calls from a DID to any pre-configured (mobile) phone number.
That's a simple solution. At which point separate telephone bills become trivial and automatic.