...We do an incremental backup every 15 minutes so that we can restore up to any 15 minute windows if necessary. ...
Ok, I'd hate to think I've missed something with regard to SQL Server, but my understanding is that there is no such thing as 'Incremental' backups, as in each 'incremental' backup adds just the changes to the database from the last 'full' or 'incremental' backup. I'm guessing this is just a mis-use of a word and you meant to say 'Differential' backup, as in each 'differential' backup contains changes to the database since the last 'full' backup.
...The nightly backup is a full backup with transaction logs so that we release the space back to the log file. ...
Are you saying here that you only back up the Trasaction Log once-a-day on or around the time you do a Full backup? As others have mentioned, Transaction Log are usually done at frequent intervals, allowing for reasonable point-in-time recovery and keeping the Transaction Log to a reasonable size, amongst a couple of other things.
...One option is to convert the server into a virtual server (VMware) where more spindles are working with the database. ...
I guess my question here would be, why can you not extend current Windows volumes (with more spindles) or add extra Volumes to your (my assumption here) Physical Server? Having a VM does not necessarily mean you will get more spindles, because it depends on what your Infrastructure Team (if you have this) allocate to you, along with many other factors such as whether Infrastructure share your 'spindles' with other applications, etc.
To give you an idea of what can be possible, one 500GB DB we have (on a physical box) backups up in just over 20 mins to a separate File Server on our estate. As to options, I can't really add much more than what Gail, Andrew, and a couple of others have said.