I can't find specific documentation if Logic Pro responds to Song Position Pointer messages and I don't have a Mac or Logic Pro to test with. If you are willing to continue testing, here are some ideas.
Make sure Logic Pro currently has a song at least a few measures long, then try sending a single Song Position Pointer message like this:
var position = 16; // in sixteenth notes (0 to 16383)
var byte_1 = position & 0x7F; // low 7 bits
var byte_2 = position >> 7; // high 7 bits
output.sendMessage([0xF2, byte_1, byte_2]);
If that has no effect, you might be able to use the Controller Assignments Expert View to assign an incoming Song Position Pointer message to move the playhead. Try the following steps:
Go to Logic Pro > Preferences > Advanced and select the Enable Complete Features checkbox (or in earlier versions, the Show Advanced Tools checkbox).
Go to Logic Pro > Control Surfaces > Controller Assignments (or press Command-K), then click the Expert View button.
In the Zone list, choose No Zone.
In the Mode list, choose No Mode.
Below the Control/Parameter list, click the + button to add a new assignment.
Fill in the following values:
Controller Assignment Parameter
Control Name: Song Position Pointer
Label: [blank]
Flip Group: none (0)
Exclusive: unchecked
Class: Global
Parameter: Playhead (Beats)
MIDI Input Message
Input: Any
Value Change: F2 Lo7 Hi7
Touch/Release: [blank]
OSC Message Paths
[blank]
Value
Min/Max: 0 127 or 0 16383 [? see note a]
Format: Unsigned
Multiply: 0.25 or 1.00 [? see note b]
Mode: Direct
a. I'm unsure if the Min/Max values are for each of the Lo7 and Hi7 bytes individually (use 0 127), or for the combined value of the Lo7 and Hi7 bytes (use 0 16383).
b. I'm unsure if the "Playhead (Beats)" parameter is expecting values in units of quarter notes (use 0.25) or in units of sixteenth notes (use 1.00). The MIDI specifications describe the Song Position Pointer is in units of sixteenth notes called "MIDI beats", so in the context of changing the song position, "beats" could possibly mean "sixteenth notes".