Most major (international) moving companies have head offices in Taiwan, but they tend to be based in Taipei. However, most of them have agents in Taichung, or are happy to send someone over to give you a quote.

Here is a list of moving companies and their contact details:

Allied Pickfords
Tel: 02 2836 1000
Asian Tigers K.C. Dat
tel: 02 8791 6606

Crown Van Lines
Tel: 02 2762 2500
Four Winds International Group
Tel: 02 2571 0564
President Van Lines
Tel: 02 2541 2163

Sea Ace
tel: 04 2314 7859

Transworld International Van Lines
Tel: 02 2836 1000