OK. Finally bit the bullet and hunted out the current version of "The Mann Act". It can be found in the U.S. Code, here:
18 U.S. Code Chapter 117 - TRANSPORTATION FOR ILLEGAL SEXUAL ACTIVITY AND RELATED CRIMES | LII / Legal Information Institute
There is a separate "sex trafficking" provision which catches associated actions that don't involve the actual "transporting": Section 1591:
18 U.S. Code § 1591 - Sex trafficking of children or by force, fraud, or coercion | LII / Legal Information Institute
In respect of victims under 18, the fact they might be happy as clams to be travelling and enthusiastic participants in the romps is irrelevant. They don't have to have been coerced or threatened in any way. The mere fact they are under 18 is enough for the person who knowingly transported them for the purpose of prostitution or any sexual activity for which any person can be charged with a criminal offense; or even with the intent to do those things; or used the mail, etc., to knowingly persuade, induce, entice, or coerce, them into engage in those activities, is enough, and renders the transporter or persuader to be fined and imprisoned for not less than 10 years or for life.
A person who attempts or conspires to knowingly transport someone under 18 with intent they engage in prostitution or any sexual activity for which any person can be charged with a criminal offense, is liable to the same penalty as if they were the one who did the transporting.
Section 1591 - the specific Sex Trafficking section which is wider than the "Mann Act" provisions - provides that a person who recruits, entices, harbors, transports, provides, obtains, or maintains by any means a person under 18 who will be caused to engage in a commercial sex act; and any person who benefits, financially or by receiving anything of value, from participation in a venture which has recruited, etc., a person under 18 who will be caused to engage in a commercial sex act; will be liable to penalties varying depending on whether the person is over or under 14. Where the victim is between 14 and 18, the penalty is a fine and imprisonment for not less than 10 years or for life. If force, threats of force, or coercion (as defined) were involved, the minimum prison term is 15 years. Again, the victim might be thoroughly enjoying everything that happened and have had no threats at all made against her, but that's irrelevant for the issue of conviction.
Section 1591 defines "commercial sex act" as any sex act, on account of which anything of value is given to or received by any person. So the "victim" doesn't have to have been paid in money.
The section defines "venture" as meaning any group of two or more individuals associated in fact, whether or not a legal entity.
Section 1591 also contains the interesting provision that, "Whoever obstructs, attempts to obstruct, or in any way interferes with or prevents the enforcement of this section, shall be fined under this title, imprisoned for a term not to exceed 20 years, or both." I find that one very interesting. I'm not sure what actions it might catch. I wonder whether letter-writing might qualify?