Building a commuter

Jimny14

So, I'm currently commuting to and from work on my old Apollo phaze mtb which I've stuck some schwalbe land cruisers (1.75 I think without checking) and we're rubbing along just fine, but I find there are limitations I'm not happy with. I dont ever get off the big front cog and am generally running in top gear running out of ability to get more speed quite a bit. The vast majority of my commute is on road but there is some toe path section which is gravelly and some bits are quite pot holey. So I've been thinking about what I need the bike to do and how to improve on what I have. Do I go buy a new bike, look around for bits second hand and build something over the next year or so or adapt the phaze more to suit my needs. I've got about £300 to put in at the moment.
Please correct me if I'm wrong but I feel I'd need a decent large frame (I'm 6' 5) although the phaze now I've raised the bars and got a longer seat post is OK, some sturdy wheels a bigger chain set than currently on and some brakes maybe stick with discs? I'm not sure. Any help appreciated