Whichever side you ground, X1 or X4 becomes your neutral. You can ground in the middle as well. The only thing that changes is terminology, X1-X4 becomes L-L instead of L-N. If you do ground the center tap you can use 120V rated insulation which. I don't think this will save any cost.

AppleJaxJap, you appear to have committed what I consider to be a common sin among engineers and technicians: only looking at the graphics and not reading the text. The table to the right of the diagram tells you exactly what to connect for each side depending on the voltages, so the simple answer to your question is yes.

xnuke
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Xnuke,
But the unanswered question is: can he ground X1 (or X4)? This isn't addressed in the text. Normally, the voltage to ground of a 240 volt wire is 120 volts because it is part of a 120/240 volt circuit with the canter point (X2-X3) grounded. NESC 250.20(B) requires a system to be grounded if the system can be grounded so that the maximum voltage to ground on the ungrounded conductors does not exceed 150 V. It's not clear to me if grounding X1 or X4 is prohibited when there is no conductor connected to X2-X3. I don't think it would be prohibited for a 2-wire circuit. Consider, though, that in a 240 V delta system with one winding mid-point grounded, there is a 208 V to ground high leg that is required to be identified by an orange color by Rule 110.15.

Quote (jghrist)

NESC 250.20(B) requires a system to be grounded if the system can be grounded so that the maximum voltage to ground on the ungrounded conductors does not exceed 150 V.

Very similar wording in the Canadian code. (Under 150 Volts to ground must be grounded.)
Consider 277/480 Volt lighting panels or in Canada, 347/600 Volt lighting panels.
You have one end of 277 Volt circuits grounded.
You need not ground one end of your circuit but you may if you wish.
I would ground X1.
If you do not ground the circuit the Canadian code requires ground detection equipment.

Quote (Canadian Code)

(2) Wiring systems supplied by an ungrounded supply shall be equipped with a suitable ground fault detection
device to indicate the presence of a ground fault.
(3) Ground fault indication activated by the ground fault detection device required by Subrule (2) shall be
clearly
(a) labelled as to its purpose; and
(b) visible to persons monitoring the status of the system.

A jumper to ground is so much cheaper and easier.

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Ohm's law
Not just a good idea;
It's the LAW!