How to replace downtube shifters with stem shifters? My bicycle has clamped downtube shifters that I would like to replace with stem shifters. Is it as straightforward as replacing the downtube shifters with cable stops, then running cable to the stem shifters?

The bottom cable stops in the frame of my bike are on opposite sides. But I've only seen double cable stops like this one where the stops are closer together. Can the cables partially "wrap" around the tube? Are there double cable stops with the stops on opposite sides? Or should I use two single stops on opposite sides? Or should I use a double cable stop at the bottom too instead of the frame stops?

Any advice would be great. Thanks!
You'll need longer cables in order to bridge the distance between where your original downtube shifters were and the stem (where the new shifters will be mounted). And you'll need to install a shifter cable housing going from your new cable stops (on the downtube where the original downtube shifters were located) to the new shifters on the stem.

If you plan on using shifters on the stem without an integrated cable stop you will have to add one just before the shifter(s) on the stem. Most likely your stem mounted shifters will have integrated cable stops though (such as can be seen in the following image) 

Make sure to cut the cable housing to the appropriate length, make sure the liner is not folded over on itself before inserting the shifter cable. Use housing end caps on the cable housing if your cable stops allow for it (if there is enough room for the cable end caps). End caps: 

It's alright if the shifter cables running from your bottom bracket towards the top of the down tube "'wrap' around the tube a bit" as long as they are not rubbing against the frame or if they are only slightly rubbing against the frame it shouldn't cause issues (it will be even less of a problem on non-indexed friction type shifters). If you find that your cables are rubbing too much on the frame/are not running smoothly because of it your suggestion of using a second cable stop on the bottom of the downtube might not be so bad. Do keep in mind that after the first cable stop your cable is already sheeted by cable housing so in this scenario I would suggest using only 1 cable stop (near the BB on the downtube) and letting the shifter cable+housing combo run all the way to your stem mounted shifters. This will most likely save you money on parts (less cable stops and brake cable housing is not that expensive especially when bought in bulk (10+m)). also this approach eliminates the posibility of the shifter cables rubbing against the downtube.

To neatly manage the cable housing in said situation I suggest using a cable clamp such as this one (dura-ace):

Mounted on a bike it looks like this:


There are also downtube mounted cable stops (clamp style) available where the two cables stops are further apart, which may match your current bike frame's cable stop spacing better. Here is an example: 

They appear to be less common though so you might have a hard time getting your hands on one.

Perhaps you could use 'braze on downtube cable stops' . If the bolts used in your current clamp on down-tube shifters (to keep the shifter handles bolted onto the 'clamp body' have the same dimensions (same thread/diameter) as the bolts used to bolt on downtube shifters to a bicycle frame with braze-on downtube shifter mounts you might be able to install these 'braze on downtube cable stops' on your original clamp on shifters to create the needed cable stop.

What braze-on downtube shifter mounts look like:



What braze-on downtube cable stops look like: