My suggestion would have been option 2 in this case. You should be able to do the forward at the registrar. This will allow you to keep your mail records at the registrar and point your mail wherever you want (either keep it at 123 reg or point it to a service like Office 365 or wherever) and your website will go where the forward points.

Another option would be to move the nameservers to the hosting company so that you would get the direct name usage, then simple create your MX records so that they point back over to where your mail is.

If you want to have the two in two places like this, you will have to compromise one or the other.

Of course, if you had a "normal hosting company" (i.e. not Magix, where you are working on a subdomain or whatever), you could just create an A record at the DNS location (where your nameservers are) pointing to the IP address of the hosting company where you site is being hosted.

There are a lot of options as long as you are using "normal" services. When you get into subdomain hosting and such it actually makes things more difficult, even though they are "cheaper".

Does that help at all?