Basically, you can't both support older devices, and have the improved security of hashes signed using the more modern algorithm.
The push to eliminate SHA-1 has been extensive, and, by the usual standards of these things, remarkably quick. This isn't a bad thing - there are well documented problems with SHA-1 signed certificates, and while these are not currently viable for most attackers, the technology is improving all the time, and it is better to have completely deprecated SHA-1 signatures before the technology reaches the dangerous point.
There is very little that can be done to handle the lack of support for older root certificates. These are designed to expire after a while, and although the expiration has been brought forward, the plan was always to eventually stop using them.
Similarly, you can't backport a certificate signature. You can, obviously, sign the same certificate with two methods, although you can only use one of them for a given web server safely (unlike ciphers, SSL doesn't negotiate signature methods).
If you could find a provider willing to sign a certificate using the SHA-1 algorithm, with the older root certificate, you could direct feature phone users to a distinct version of the site using this, while other users get a version signed with the newer algorithm. In order to do this, you would need to have your landing page either running over HTTP, or signed with the older certificate, then redirect from there. If you sign it with the newer certificate, the older devices won't be able to access it, so will never reach the redirection.
This does present a security risk, but this might be considered acceptable, and the difficultly of finding a willing and able CA remains.
The other option would be to perform a similar operation, but self-sign the certificate for these devices. This doesn't solve the root certificate issue, but may allow for an encrypted connection, if users can manually accept the certificate (I don't know whether this is always possible on feature phones - been a while since I tried). This provides confidentiality without implicit trust provided by a CA, but you get to control the signature and other features of the certificate.