OK... One, there are no "agreements" anywhere. I don't know where y'all got this idea, but agreements between ISPs for helping deliverability
do not exist. Case in point, Aweber's integration of SpamAssassin scoring... which is wonderful, by the way... the only thing affecting the SA score is how you build your e-mail, plus the mail server score.
The mail server score has nothing to do with "agreements" either.

The mail server score depends on elements like RBL listings, spam history, Exim configuration, SPF record present/absent, etc. It's all how the tech geeks have your server's software configured.
Repeat after me:
THERE ARE NO AGREEMENTS.
Honestly, the ideas folks will "buy into" these days is unreal.
What's more,
Aweber's IP space has at least 2 spam blacklistings which
is going to cause deliverability problems with some ISPs -- no way around that. RBLs are killers. If you're going to mail out, it is
imperitive to put your website on clean IPs.
Can you run the kind of script you describe, and have good deliverability statistics? Absolutely!!! The script you're looking for is called
1-2-All by Active Campaign. Several of my clients run 1-2-All, and I also run my gift shop's lists on it, and it is
fantastic. And yes -- you can schedule mailings to take place at certain times post-subscription. I have a client who did this for Daytona Speedweeks in February, she runs a NASCAR-related list, and all new subscribers received a "free Speedweeks TV schedule" -- which was simply programmed in to send 20 minutes after they signed up.
1-2-All Lite is a one-time buy -- not recurring like Aweber. It's $97 one-time, which enables you to run up to 4 lists and set up 2 admin users. Or, you can get the full license for $159. I will tell you this:
it is worth every penny. It is a professional, enterprise-class solution and outdoes easily 99% of the scripts that you'd install on a hosting account, hands-down. (And in terms of the scripts that are run on a Linux server, I've tried them all -- including
Mojo Mail/DadaMail,
Mailman,
phpList, etc.)
I've specialized in mailing list scripts & how to run them successfully on servers, for years. I ran the Mojohelp.com forums, which was a community support site for Mojo Mail (now known as DadaMail) before the developer finally put his own forums back up. I mention this because we got pretty deep into mail server configuration and how to build/tweak the script to improve deliverability rates. This has always been a big issue for website owners who wanted to run their own mailing lists.
Anyway, if you don't want to add another $20 to your monthly internet fees, and you want to run your own list software (where you have at least somewhat more control of whether your IPs are blacklisted)
1-2-All absolutely will meet your needs. It's a one-time license fee and you can install it on your existing hosting account.
I should mention that deliverability rates
will be affected by the sending OS. If you are on Windows and having deliverability issues with scripts (not uncommon), move to Linux, and choose a Linux server which properly accomodates your sending script. (Your host/prospective host should be able to help you with this) In the case of 1-2-All, for example, it hooks perfectly into Linux servers running cPanel, no tweaks or special configurations are necessary.
If you guys have any questions at all, please feel free to pick my brain.

Always happy to help however I can!
(And see, I didn't even put my affiliate links in. I wanted my script recommendation to be a totally "clean" and earnest one.)

Bailey