what other strategies could a business employ to cope with the changes in costs created by the tariff?

Question

Apart from moving production elsewhere

Answer 1

Smuggling is the classic answer whether the tariffs are against imported goods or taxes against local produce (think moonshiners)
http://en.wikipedia.org/wiki/Smuggling

Then there is the option of declaring a false value. One form of this is to import almost completed goods which would be worth nothing on the open market but are worth plenty to the importer because he has what it takes to finish the manufacturing.

(One classic example was an importer that bought 50,000 pairs of leather gloves. He had them paired left with left and right with right and shipped separately. He paid the tariff on 25,000 pairs of right with right, but not on the shipment of left pairs. U.S. Customs auctioned them off for non-payment of tarriff,; and since no one wanted 50,000 left handed gloves, the importer bought them for far less than the tariff would have been.)

A variation is declaring that the goods are in a different category than they really are:
http://www.tradediversion.net/archives/2007/11/tariff_evasion.html


And there is the option of applying political pressure to get an exception made. For example, the "big three" U.S. automakers got the government to accept Canadian-made cars and parts as U.S. made for purposes of labeling. Similarly, bananas from former European colonies get tariff breaks into the EU.
http://www.caycompass.com/cgi-bin/CFPnews.cgi?ID=1027095

Then there is the case of quotas with high tariffs for exceeding them. The answer then is to ship through another country with an unfilled quota. China has done this for years with textiles:
http://www.aeaweb.org/annual_mtg_papers/2006/0106_1430_1202.pdf

The list goes on.

Human beings are incredibly inventive, aren't they?