In filing a hypothetical federal civil case, it seems like some forum
shopping may be possible. Might one of the reasons to select a
particular court be to seek a speedier or slower trial?
When more than one forum is possible, this is routinely a consideration. But, most of the the forum shopping between forums is between filing in federal court (which is usually slower) and filing in state court (which is usually faster). An ability to chose between several different federal courts is the exception rather than the rule.
Of course, speed is usually a secondary consideration. The likelihood of a decision maker to rule in your favor (i.e. the jury pool in a case with a jury trial, and the range of potential judges in a case where the key decisions will be made by a judge) is almost always more important. This can be due to the legal precedents and local rules that apply in the respective forums (e.g. due to circuit splits of authority) and due to the differences in the expected biases of the decision-makers on a case by case basis.
A tertiary consideration is convenience to the lawyers making the choice of forum decision.
While official statistics are available, it would be common for lawyers to informally survey lawyers who practice in the respective courts about likely times of disposition for a specific type of case. Not all kinds of cases proceed at the same speed.