Secondary domain redirection via 301

Is there anyway to make this work:

Our current site is ancient, hosted elsewhere and served up via their proprietary CMS.  The url is http not https (no ssl).

Our idea - create a squarespace site to replace the ancient site and use a different domain name.  Said different domain was redirecting at the dns level to the ancient site's domain anyway.

Here's the problem, the ancient site has over 140 Google indexed pages and there are several links to it from various articles all over the web. Let's call it http://ourOLDsite.com.

I went to the http://ourOLDsite.com's proprietary cms and added 140ish 301s like this:

http://ourOLDsite.com/variousindexedurls  ->  https://ourNEWsite.com/newhomeforthoseurls    They don't match up page for page -that ancient site was super bloated.

So now, I would like to use ourOLDsite.com as a second domain name for the squarespace content located at https://ourNEWsite.com  and get rid of that old hosting provider.

Can I do this and keep some of my SEO, keeping in mind that the ourOLDsite is http?

Can I do 301 redirects on a squarespace secondary domain - it doesn't look like it?

Do I have to keep the old hosting with its 301s until Google forgets about those old links and then make it a secondary domain for my new squarespace site?

What do it do?   🙂

I hope this makes sense and I would appreciate any responses.

Thanks!!

I need to add that the new squarespace site was created, is up and running and looks great at https://ourNEWsite.com (not the real URL - used for purposes of this post along with other url in the forum post.)