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No, moving them for something as little as that will do much more damage than good. Eventually, the pot will become too crowded, which at that time will be when you will transplant, divide, or do other yearly maintenance.

I would let it continue on until it, absolutely, needs to be moved.

Here is an article that will help you with Caladium care:

https://www.gardeningknowhow.com/ornamental/bulbs/caladium/caladium-plant-care.htm

You won't have time for them to grow and store energy before you have to dig them up for the winter, if you plant them now.

These plants are only suited for outdoor beds in zones 9 and up. They will not survive winter, in-ground, in your area.

Alternatively, you can plant them in container, and grow them indoors over winter. Then you can plant them out in spring, next year.

Here are some articles that will help:

https://www.gardeningknowhow.com/ornamental/bulbs/caladium/caladium-plant-care.htm

https://www.gardeningknowhow.com/ornamental/bulbs/caladium/growing-caladiums-indoors.htm

We have the perfect article for you, here:

https://www.gardeningknowhow.com/ornamental/bulbs/caladium/when-to-plant-caladium-bulbs.htm

After you dig up the caladium bulbs, leave the soil and foliage attached and put them in a cool, dark place for 2 to 3 weeks while the bulb is "curing" or going dormant. Then, cut the tops off even with where the soil line was and brush off any loose soil. Then apply a fungicide and store the bulbs in a frost-free area for the winter. You can store them in sand or sawdust to keep them from getting too dry.

Austin is in hardiness zones 8b and 9a. If you are in the 9a area, you should be able to overwinter your caladiums outside with just a heavy mulch.

Unless your winter temps get much below freezing, you can leave caladium bulbs in the ground. They can tolerate down to -6 C (20 F) with a heavy mulch. When you do store them, it helps to cure them first and spray with a fungicide. Then they should be kept in sawdust or sand to prevent them from drying out completely.

I imagine yours dried out too much. Here are the winter care instructions:
https://www.gardeningknowhow.com/ornamental/bulbs/caladium/caladium-care-in-winter.htm

Grafting bulbs together, usually, doesn't work too well. Something like this can be done in a sterile lab, but this is not feasible for the home environment.

You can plant them in a large container together, however.

Yellowing leaves can be a sign of many different issues, so it will be hard to say why they are yellowing. The usual suspects are not enough light, too much water, and pH issues, but this can also be a sign of actual nutrient deficiencies.

Here are some articles that will help:

https://www.gardeningknowhow.com/ornamental/bulbs/caladium/do-caladiums-bloom.htm

https://www.gardeningknowhow.com/ornamental/bulbs/caladium/caladium-plant-care.htm

https://www.gardeningknowhow.com/ornamental/bulbs/caladium/growing-caladiums-indoors.htm