Daniel M. you're right to care deeply about this need. And I ran into the exact same Salesloft limitation in a prior role. Not only that, but they clearly have security gaps. I agree with Harshil B. that your best bet for email deliverability strength is going to be instantly.ai or smartlead.com. However, the better question it seems is "why run email sequences via your reps at all?" Those should be centralized. Reps should be emailing only when they have deep research (which they can do manually via TLD) or as follow-ups, but bulk sending should be a centralized (GTM engineering type) effort. The cost/benefit is stark: it is a major distraction to running call sequences (Nooks) and email sequences from another tool and trying to manage everything cohesively. Outreach is a great tool too but it doesn't optimize for deliverability, shamefully so given how the times have changed.
If you DO insist that reps need to be able to bulk sequence, then with your requirements, I'm surprised no one has mentioned Apollo. Nooks integration. 15 inboxes per rep. etc etc.
In your shoes though, I'd rebuild my org around 1-2 people running bulk email, SDRs doing power dialing only on high quality data, AI research>manual outreach for AEs+SDRs both ("we spoke to a couple people in your org and it sounds like March is a big month in terms of ..."), and killer follow-up/engagement signals that get actioned in bulk (GTM eng org) or one at a time (SDR/AE based on ownership/territories).
Don't forget to that getting a DMARC policy all the way to p=reject on a primary domain is a necessity any route you go. Takes a ton of work, we just went through it at TitanX, but the gains to your not-hitting-spam are immense.
