Stress in the -ing form of verbs with initial-stress-derived nouns

The only rule about stress for the -ing form of a verb is that it falls in the same place as in the other forms of the verb.

The verbs that you mention don't actually change their stressed syllable in the -ing form.

Procéss and prócess are two different verbs with different meanings: procéss has a meaning like "to move in a procession" and prócess has a meaning like "to change something for some purpose". Their -ing forms are procéssing and prócessing respectively. The -ing form procéssing is probably more often encountered as present participle ("They were procéssing down the street") than as a gerund, since the noun procéssion is used to refer to the action of procéssing. (In fact, according to the Oxford English Dictionary, the verb procéss is derived from the noun procéssion.) The -ing form prócessing has the same form as a commonly used deverbal noun prócessing.

Transport is one verb with two pronunciations: tránsport and transpórt. Either pronunciation can be used in any of the forms of the verb, so both tránsporting and transpórting exist, as well as tránsported and transpórted. The pronunciation of the verb as tránsport may be due to influence from the noun tránsport, but it can be used in any form of the verb, not just the -ing form. Another verb that can have the stress placed on either syllable with no difference in meaning is transfer.