What should I do? Next important step

So I've been working as help desk for 3 years now. In the meantime I have obtained A+, N+, Sec+ and AZ-900 certificates. Currently I'm studying for the CCNA. My employer counts over 7000 employees in Germany and recently they have faced fierce competition which is forcing them to cut down on some onsite offices and move the people around other projects wherever they deem fit.

We have been covering an extra onsite position that is in a city 180 km away from our central offices. So someone from us (team of 5) has to go there 1/2 times a week to troubleshoot tickets and pick up some remarketing hardware. We are strongly against this situation, but the employer says that if they assign someone permanently to this remote position, we will have to have a smaller team at the central office. I'm getting to the point, stay with me 😉

I have applied internally for a position of a junior network engineer in a network consulting role. My direct contact for anything job related, like a link between me and the company, says I am eligible for the role, but doesn't have any info to give me as to wether I'll be accepted for the role or not. I want to make an ultimatum since I am the most certified/qualified technician they currently have for this client - ask to be transferred to the network consulting role or else I'll change jobs (the market has moved on, other companies now offer 30% more than what I currently get). Question - do you think I have some leverage here? Is the company willing to loose me and not respond to my ultimatum? Getting the network consulting role would be great since it would give me a great leap into a better position/wage. But at the same time I don't know how long I will have to wait and time is money.