Single-Member LLC EIN vs Sole Proprietor EIN as it pertains to the W9 form

I know variations of this question have come up before, but I'm hoping to seek some additional clarity.

Apologies for the long-winded post… Hopefully this clearly explains my predicament!

I operate as a single-member LLC (I am registered with my state) and I file my taxes as an individual. I am a freelancer in the film/tv/commercial industry and I work for many different companies throughout the year. Some companies 1099 me and some require that I be W2'd and paid through their payroll provider.

I have an EIN that is tied to my single-member LLC.

There used to be some ambiguity around whether you could/should enter the company EIN on your W9, however, the most recent update to the W9 form seems to have clarified that you SHOULD NOT enter the company EIN. Instead, you must use the owner's SSN or an EIN tied to the owner, not the company:

"If you are a single-member LLC that is disregarded as an entity separate from its owner, enter the owner’s SSN (or EIN, if the owner has one). If the LLC is classified as a corporation or partnership, enter the entity’s EIN."

I know the IRS will probably be able to match my company EIN to my personal SSN, however, I am trying to make sure I do things right.

The issue I have run into on a few recent jobs is that I would like to be paid through my LLC, but in order to do so, the client's payroll service provider is insisting that I provide a W9 with an EIN and not an SSN.

My thought was that I could simply apply for a Sole Proprietor EIN and use that number on my W9, however, reviewing the language on the IRS website website, it sounds like they don't want me to apply for a Sole Proprietor EIN if I already have an LLC: https://sa.www4.irs.gov/applyein/legalStructure

"The business cannot be incorporated or registered with the state as a limited liability company (LLC)"

Has anyone run into a similar situation? Would love to hear thoughts. I am also reaching out to the IRS for clarification, however, I'd be shocked if I receive a timely response.

Thanks!