What if you approach the VOR station such that your turn OB is not on the holding side?
The picture and your description do not really match. The hold represented is a standard, right-turn holding pattern. It is probably meant as a holding pattern of the missed approach. It is not meant as a holding pattern for before you travel outbound for your procedure turn. Based on the standardized format of IAPs, the right-most triangle is the Final Approach Fix. The left-most triangle is the Intermediate Fix. The VOR is an Initial Approach Fix. If, for some reason, you have to hold above the VOR prior to joining the approach, do so at or above the IAF altitude and intercept the outbound radial by continuing your turn after the outbound leg. I would warn against holding over VORs without ATC providing aircraft separation. VORs are busy airspace.

The IAF will have an altitude associated with it at which you can approach the IAF from any direction and be clear of obstacles. If one is not present, approach the IAF at or above the MSA. If that were not the case, the IAP would have a notation designating the IAP Not Applicable/Available coming from certain directions. For instance, flying from left to right on the picture, ATC would clear you to start the IAP at the IF (which can be designated on the chart as an IF/IAF) instead of the IAF (VOR). Aircraft flying from all other directions would fly to the VOR to start the IAP. The IAF, procedure turn, IF (IF/IAF), and FAF would all have their respective altitudes assigned to them in that order. Your profile view would start with the altitude at which you would need to stay above in order to start your procedure turn. If not, start at your MSA and descend down to the PT altitude.

Something else that comes to mind is checking the sectional and charts for the MSA and whether the IAF is a mandatory fly over fix. If it is not, turning onto the indicated radial in a way to intercept it prior to crossing over the VOR would expedite your IAP. Depending on your speed and original heading, you would start your turn a quarter to a full mile out before reaching the VOR or radial.

Also, “the protected side of a hold“ is a misnomer. There is no such thing. There is a holding-side and a nonholding-side. The entire area around the hold is protected airspace based on the dimensions of the hold. See the following question:
what are the dimensions of the protected space provided by a holding pattern