Short answer: No, there's no way to have the benefit of Strict SameSite without the drawbacks of Strict SameSite. However, you can get most of the benefits (and fewer drawbacks) by using Lax SameSite.
I think you quite badly misread that article you linked. Google is not, and has no plans to, change the default SameSite behavior to Strict. All they are doing is changing the default to "Lax" and adding "None" as a new option to override this default. ASP.NET is making no changes except adding the
None to the enum values.
The concern is that, if you send
SameSite=None to a browser that doesn't yet know about this value, it will interpret it as
SameSite=Strict because that's what the standard says to do when the value isn't recognized. Therefore, IF and ONLY IF you DON'T want to use SameSite at all, you will need to do user-agent sniffing to determine "this browser still defaults to no SameSite and will freak if I say
SameSite=None" vs. "this browser defaults to lax SameSite and I need to tell it to not do that".
If you expect top-level navigation from other sites to yours, but do not expect to need cross-site authenticated requests other than top-level GET navigation, then you should already be setting
SameSite=Lax, and this change (neither Google's change nor ASP.NET's change) has no impact on you.
If you are already using Lax SameSite, you literally don't need to do anything at all (I guess you could save a few bytes by sniffing new Chrome builds and not sending the now-redundant header, but it's probably not worth the effort).
If you actually want to use Strict SameSite, do it exactly the way you would today; nothing has changed there either.
As a final word of advice, bear in mind that there are still a lot of people using outdated browsers that don't support SameSite at all. It's potentially valuable as a defense-in-depth measure against CSRF, the same way CSP is a defense-in-depth against XSS, but you still need some other anti-CSRF mechanism for anybody on browsers that don't support SameSite, unless you block all such browsers from signing in at all.