Changing rear cassette

[Ajax Bay]

I would have thought this CX50 46-36 would do you, Steve, or similar:
https://www.chainreactioncycles.com/shimano-105-cx50-double-10sp-chainset-black/rp-prod70118
And buy a 30t ring (110mm BCD 5 bolt, Spa Cycles or elsewhere) to replace the 36t for your hilly trip (the 36t will be fine for your home roads).
The FD will handle a 16t front difference (you have 50-34 now) but the FD will need to drop down a bit and the cage curvature will not fit quite as well, but will work OK.

 

[DCBassman]

To illustrate what can be made to work, my Scott us running a big road triple 52-42-30 onto an 8-speed 11-34t cassette, using a GS medium cage Sora 3300 mech. I've used a hanger extender (cheap Chinese one, seems fine). But it is at the very stretched limit!

 

[Mr Celine]

Another vote for a triple. My Roubaix has 10 speed 105, 50 39 30 at the front and 12 -27 at the back. For a trip to the Alps last year I swapped the granny ring for a 28.

Got up hills no bother. Anything lower and I would have been struggling to keep the front wheel on the ground.

The downside is you'd need a new chainset and front shifter.

 

[andrew_s]

Changing the inner chainring to 28T would reduce the lowest gear by a bit more than the 42T sprocket would (21.0" vs 21.8").
This would require a replacement chainset.

Unfortunately sub-compact doubles are rare at present.
Shimano recently announced a gravel bike groupset (GRX) but as yet there's only a 46/30 option, which doesn't go as low (22.5").

A couple of people (Velo Orange, SunXCD) are selling modern versions of the Stronglight 49D/TA Pro Vis 5 50.4 BCD chainsets, which can come as a 46/28 double, with a fairly narrow Q, but they aren't cheap (and are square taper).

The relatively cheap option is to use the inner and middle positions of a triple, This is usually done using a bash guard in place of the outer, but you could get shorter bolts or use a spacer under the chainring bolt head (I used the tabs off an old chainring when I used an available triple as single ring fixed).

It's easier if you can fit a square taper BB (i.e.BSA68 threaded frame) as there's more choice of cheap chainsets, and you can fiddle with the chainline, which would probably be different (further out) using a triple.

Using a triple as a triple would require a change of shifters (probably - bar end shifters and some Campag Ergolevers would be OK).

 

[twentysix by twentyfive]

I run a Triple. 44-34-24 with a 9 speed cassette 14-25. That's worked for me for many years but I've found the hills to be getting harder to ride so I've put together my own cassette from two. So now I can run 16-36. Needed an extender for the rear mech but bizarrely I found the existing chain was too long (on small - small). It all worked fine tho'. Got me up and down the Dolomites.

 

[Dogtrousers]

Just as an aside, dropping the gearing can have unintended consequences(especially if you are a lazy sod like me). I dropped the gearing on my bike by a couple of inches (34/32 to 34/34). I found that the big hills didn't feel any different, I still laboured up them ... I just went slower. And it took longer.

This is because I approached them just the same - slap it into bottom gear and adopt grindy cadence. If I'd made a bit more effort I could have got up the hills in the same time while turning the pedals a bit quicker. But being a creature of habit, and lazy, I just tend to drop down to a standard climbing cadence, switch off brain and hope that the top will eventually come.

Since noticing that I do try to put in a bit more effort, but it's easy to just switch off.

 

[andrew_s]

I would have thought this CX50 46-36 would do you, Steve, or similar:
https://www.chainreactioncycles.com/shimano-105-cx50-double-10sp-chainset-black/rp-prod70118
And buy a 30t ring (110mm BCD 5 bolt, Spa Cycles or elsewhere) to replace the 36t for your hilly trip (the 36t will be fine for your home roads).

No good.
You can't fit smaller than 34T on 110 mm BCD

 

[Ajax Bay]

No good. You can't fit smaller than 34T on 110 mm BCD

I'm wrong. The smallest 110mm BCD chainring is 33t.
Spa Cycles and Wiggle.
The OP wants to stick to a double, though.

 

[si_c]

If you're willing to use oval chainrings Absolute Black do a 46/30 or 48/32 oval chainrings which fit a standard Shimano compact crankset. They're not cheap however.

Your best option in terms of crankset is probably to either swap to an MTB chainset or square taper and find appropriately low rings.