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While it might be questionable, throwing away a well-aged domain, it sure sounds like it's causing you some other issues, including bounce rate issues for people who find you simply because of partial domain name match against their queries. I'd be inclined to take the hit on domain age and move to the new site.  301 redirect the old site's pages to corresponding pages on the new site.  You can set up your old email address to forward to your new one, so people using the old will still get to you fine.  I wouldn't use the old email address on the new site, as you'll get people ignoring your emails because it's not from a site they recognize.

Glad you got it sorted out. If you're 301-redirecting a lot of domains, I'd suggest doing it gradually or maybe holding off on the lowest-quality domains. Google can see a massive set of redirects as a bit of a red flag (too many people have bought up cheap domains and 301-redirected to consolidate the link equity). If the domains are really all closely related or if you're only talking about a handful (<5) then it's probably not a big issue.

Thanks to everyone for the comments and suggestions. So, to be sure I am doing this correctly. I am building a totally new site. I will probably continue to use my primary domain name, even though it really has no relationship to my business in terms of key words. It has been out there for over 20 years and has domain authority of either 18 or 30 and authority of 21. The domain authority of 18 or 30 depends on whether you are talking about XXXX.com or XXXX.com/index.html. Obviously this is another issue that I need to address. I have an early version of the new site out there on the net, and Moz is telling me that I have a problem with duplicate pages. It is the same issue, YYY.com or YYY.com/index.html. (This is a new domain name that I am presently only using for testing, although it does contain excellent keywords in the domain name.) My next question refers to 301 redirects or canonical. I suspect canonical is easier. The question is, which is the best canonical page, YYY.com or YYY.com/indexhtml? I assume YYY.com, since there will be many other pages such as YYY.com/info.html, YYY.com/services.html, etc. My plan is to make many pages that will refer to various services that are also keywords, such as YYY.com/keyword-phrase-A.html, yyy.com/keyword-phrase-B.html, etc. I assume this is the best way. Also, I will have a number of instructional white-papers that will be keyword rich.