Best option to upgrade 7-speed bike to higher gears I have recently bought Giant Escape 3 hybrid bike that came with:

Shimano FC-TY501 28/38/48 chainset 8/7/6-speed compatible
Shimano Tourney RD-TY500 7/6-speed rear derailleur
Shimano MF-TZ31 14-34T &quot;cassette&quot;

I find the gears are too low for my needs. I don't use the smallest chainwheel and I don't use the biggest sprocket either.
I thought I could quickly solve the problem low-cost by upgrading to CS-HG41 11-28T cassette but once I got round to removing the block it turned out that the &quot;cassette&quot; on the bike was in fact a freewheel. Bugger!
Apparently Shimano used to make FW726 11-28T freewheel but they are nowhere to be found.
How to solve this pickle? I'm thinking my options are:

Replace the wheels with a set that comes with a 10 speed freehub, since replacing the hub alone would probably be close to the price a new wheelset if you consider the fitting cost and I wouldn't do it myself. Get a spacer and fit my CS-HG41 onto it.
I'm perfectly fine with having 7 gears at the back and this would give me an opportunity for a further upgrade in the future should I ever needed it. It also seems the least fuss option.

Replace the existing triple chainset with a double 34-50T compact or 36-52T semi-compact crankset (e.g. Shimano FC-A070 or maybe even FC-2300 both matching the existing chain and bottom bracket)
The frame seems to have enough clearance for such upgrade but I guess I would have to replace the front shifter and possibly (?) the front derailleur too.


Does it sound like the right approach? Can you think of any other options?
Adding two or four teeth to the largest chainring will not improve you high gear very much.  Right now your highest ratio is 48/14=3.429.  Going to 52 will get you to 52/14=3.714, which is not much of an improvement.  It is better to focus on the rear, where 48/11=4.364  

Going to a new wheel set you need to check that the wheel is the proper width for the frame.  The space between the lugs might be 126,130, or 135 mm.