The issue of fax modems not working over digital phone lines (i.e. VoIP) is a very common one. The underlying reason is fairly complex, but the bottom line is that VoIP networks were designed to transport voice audio, not modem audio. The two are very different and the "tricks" uses to make voice work over an IP network actually make modems fail.
This is one of the things we set out to fix at FaxLogic. We know that many companies want to keep their existing fax machines (there are lots of reasons, but the biggest may be that as long as there are paper documents that need to be shared, it's hard to beat the convenience of a fax machine). In any case, we support plain analog fax machines with our Internet Fax Adapter (a small device that connects the fax machine to your network), and give them all the capabilities and benefits of a dedicated fax server (but offered as a low-cost, cloud-based service). You loose the phone line (and the cost), keep your number, and keep faxing like you always have (with the added benefit of capturing all your faxes in our secure web-based portal, as well as getting fax-to-email, email-to-fax, web-to-fax, etc.) And if you like, you can configure inbound faxes to be delivered via web or email, using your fax machine only for sending faxes. It's an ideal "best of all worlds" solution, and works perfectly in environments like yours that have VoIP phone service.
On the issue of junk fax blocking, frankly, it's tricky. Like some other providers, we will let you designate certain phone numbers (based on Caller ID, for example) to block or send to your spam folder. But the problem is that many junk-faxers use different Caller IDs over time, or worse, no Caller ID at all. And while you could block all "no Caller ID" faxes, this isn't practical because there are many "legitimate" senders that don't send Caller ID. And to make matters worse, some Internet Fax providers use a common set of numbers as their Caller ID, across all of their customers. So all in all, no practical solution will eliminate all of the junk fax you receive.