That’s a rough one, primarily because the situation you just described, coupled with the ignorance of what constitutes spam, in general, on the part of many (most?) marketers (your clients) is a “classic” recipe for spamming.
As far as I know, for what you are describing you will most likely end up having to use a “spam friendly” mail service (there are several, but I won’t tout them here); doing that will most likely get you TOSsed in relatively short order from DH if that spam can be related in any way to a DH hosted site.
While your intentions may be entirely “legit”, you won’t be able to control your clients with a system set up the way you describe, and, to a certain degree, you will be blamed for what they do.
Your alternatives are the same as any “spammer”; find spam friendly hosting and mail service (increasingly harder to do, thankfully!), or run your own web and email server (which will most likely be quickly blocked by many providers); rinse, and repeat as necessary when booted or no longer functional.
Not real encouraging, I know, but that is how I view the current state of affairs. Good Luck!