Request for a Separate Persian Language Engine for Adobe Software

All of these things that you're described sound like they would be uncontroversial and important improvement to any page layout app. However, they don't seem like they need specific treatment for Persian language alone. All right-to-left languages that can be laid out in InDesign share these issues, to some extent.

I encourage you to post bug reports and feature requests over at indesign.uservoice.com, but I don't personally believe that the InDesign dev team is likely to build a whole new text composition subsystem for Persian, specifically. It doesn't fit that well with the current InDesign model of having different composers for different kinds of text. There's a "J Composer" for Japanese that also handles Chinese and Korean grid layout, and the "World-Ready Composer" for right-to-left scripts, and complex South Asian and Southeast Asian scripts. I don't know what the future roadmap looks like for InDesign's handling of complex scripts, but that structure doesn't seem like it's going to have language-specific subsystems in it. No harm in asking, but if your goal is "better Persian layout in InDesign" then I think that you might want to familiarlize yourself with the current feature request system at use in the development of InDesign, and adjust your strategy to fit. 

Accordingly, I think that your best way forward, if you want to pursue improving Persian layout tools in InDesign, is going to be to 

1) Present some specific issues, with screenshots

2) Post these issues to the Uservoice

3) Mobilize your community of people doing Persian layout to go and vote up those issues you've posted to the Uservoice

3b) also post those issues here, as I know I'm not the only person working with complex scripts in InDesign who would like to see improviements, and who will immediately go and vote up any issue even vaguely related to my work

4) Actively look for people on the Internet who are having problems with Persian layout in InDesign and publicly posting them, help those people, and then tell them "Oh by the way, please go sign up for Uservoice and vote up these particular issues that, once addressed by the InDesign dev team, will make Persian layout better." 

I have some specific responses to your descriptions of these issues below:

Word Joining/Breaking:

Persian text often has issues with the correct joining of characters (especially in initial, medial, and final forms of letters) when OpenType settings are not properly configured. This can result in incorrect or inconsistent word connections.

I don't think that there is anything unique about Persian in InDesign, here. That statement sounds like it applies to Arabic, Dari, Pashto, and Urdu as well. I'd love to see some specific examples, though. 

Punctuation:

Persian punctuation marks (like commas, periods, quotation marks) often do not align properly with the text, especially when mixing Persian with English text. There are cases where punctuation marks need to be adjusted manually for correct positioning.

I tend to use automation (e.g. a GREP style) to finesse the appearance of Latin-script punctuation in the middle of Persian (Arabic, Dari, Pashto, Urdu) text. If you can post an example, I'd be happy to suggest a technique that will allow you to skip the manual positioning of punctuation. But, broadly speaking, issues like these usually come from the font metrics. If you can show us some cases where the punctuation in mixed Persian/English text is consistently handled incorrectly in InDesign, in a variety of different fonts, but consistently renders correctly in a different app using the same font(s), you may have a case regarding which it'd be worth filing a bug report.

But most of my work is in complex-script languages, with lots of parenthetical English as the documents are meant to be used in the US, and making the Latin-script parenthetica text look decent next to the Arabic/Burmese/Chinese/Dari/Estonian/Faerorese/Georgian/et cetera is usually a challenge in any language. In cases where it's easy, it's almost always because the font's Latin block was designed well. 

Ligature Issues:

Certain ligatures in Persian fonts might not be displayed correctly unless specific features are enabled in OpenType or font settings. This often results in visual inconsistencies.

That sounds more like a font problem than an issue with the World-Ready Composer or with Harfbuzz, but without a specific example it's impossible to say. Once again, this sounds like working in any one of a number of languages in InDesign - here I am saying "Arabic, Dari, Pashto, Urdu" again.

I'm not saying that InDesign couldn't handle Persian layout better, but I am fairly well convinced that there's nothing unique about how well or poorly Persian language in particular is handled in InDesign. But, once again, I'm not literate in the language, so my take has relatively little weight. If my take is incorrect, I would be absolutely thrilled to see some examples demonstrating this. 

Would you happen to know of any additional settings or features that might help improve Persian typography even further in the ME version of Adobe apps?

I've never used it before, but I've read a few positive reviews of Manzar by people who work with nastaliq. I'm not a ScribeDOOR user, but I'm aquainted with people who have been doing right-to-left layout since the Creative Suite era when all ME Editions were made by Winsoft, and there are a few of those who swear by ScribeDOOR and tell me that it's much faster and easier to use it than it is to use the native InDesign RTL tools.