It seems to me that your problem is only probably partly to do with testing and is partly to do with organisation.
Our situation is rather different to yours, as we are a specialist software house with a product that is in widespread use worldwide. Our user base is highly skilled and we actively seek feedback and suggestions for enhancements beyond the usual run of bugs being reported. This does mean that we have a continuous process of building new features into the application and these are developed and released on roughly a monthly basis. (Some features take longer to build and test than others; we have to take a business decision over the timing of new feature releases.)
So our individual new features are treated as stand-alone projects which are built, tested and deployed in isolation, Obviously, each feature has its own workflow which is tested as extensively as possible within each monthly release cycle. But unless an issue is identified during that process that might impact another part of the overall application, we do not go back and perform a full regression test of the whole product.
The way our production and interim (test) builds are structured means that new features are always tested on a build which is based on the last version to be put into production. Once all new features have been tested on a build, that build is committed to production. That way, a certain amount of regression testing is built into the process; any major breakage caused by deployment of new code would be spotted early on.
However, once a year, we do schedule a full regression test (which I suspect is equivalent to your “end-to-end” test). That is built into our release timetable and is there to ensure that each month’s incremental releases haven’t impacted something already in deployment. (Our product is quite complex and there’s a lot of stuff in it that users might only use once a year; so some regression faults might take some time to find and troubleshoot otherwise.)
I don’t know how helpful that is to you, but this seems to work for us.