1. The starting point is to consider your client's corporate culture, not what suits you best. How will your client regard your ask that you be permitted to pay up to a more expensive fare basis on another carrier? If this costs you business, only you can determine whether loss of goodwill is worth a couple of miles.
2. You are traveling in J. So, premium seating, no luggage charges, lounge access, priority security, boarding and so on. The sole value of flying different carriers may be marginal differences in the J product and an accumulation of miles in one program.
3. So, do the corporate culture analysis, consider asking about buying up yourself and don't spend another minute on the issue.
4. This would be a bigger deal if "least expensive" meant steerage on a 2-stop flight through some place 1,500 miles out of the way. But, this isn't.