If the participant’s server environment restricts email delivery, do you think it would be possible to configure this from our side?
Despite providing a "clean" email server that follows the rules, is not in a bad neighborhood and clean Email content, there is very little you can do.
In my opinion, it all comes down to the SMTP server that you use. If the SMTP server is configured well and on a clean IP or not in a bad neighborhood (IP range with a lot of spam cases).
You would need to speak with the admin of the email server on the other side to understand what is going on.
We had a similar case some years ago, where we were sending email invites to employees of a company (our client was exactly that company, who had hired us to do this research with their employees). So we talked to their IT department to make sure that our mails will reach them.
Different companies have different approaches to spam / receiving mass emails. Some important things to consider:
1. Make sure that you have a good contact list with valid email addresses. Many email servers put you on a block list when you send a lot of emails to accounts that do not exist (e.g. old emails that do not exist anymore, typos, etc.)
2. Make sure to not sent all emails all at once, send them in different steps, small tranches.
but as I said: Sending mass emails is an art in itself. You are always on the verge to be considered spam. If you send too many emails, users might report you as spam. If the text is using "fishy" language - spam filter. If you send emails from a server located in a "bad neighborhood" - spam filter. if you have a lot of emails bouncing - spam filter. If you have a lot of links in your email - spam filter.
It is tricky. Email is almost dead because of all the spam.