I have a question: How do people even have real counteroffers? Do you apply for multiple jobs and two or more happen to make you an offer? How do you manage to get the times to line up so perfectly?
Well, when you go job searching you don't just apply for one job, do you? So the timing is the interesting part. In my experience, companies want you to be open with them about this, so that they do not lose good candidates by being too slow. If you tell them you're interviewing elsewhere or entertaining other offers, they will take that into account. You can straight up tell them what your timeline is like and they will work to accommodate it.
(Of course if they're not interested in you anyway it doesn't matter how many offers you have.)
Remember, recruiting is a job too. The people who do it at the company want to hire you, they want to get those positions filled, that means they are doing their job well.
Or you can just lie about it, as OP did. Perhaps a risky maneuver, but if it's plausible for you to be in demand, I don't see why it's not worth trying.
Personally my approach is a bit more basic. I ask for what I want, and if you don't wanna give it to me then fine, someone else will. But, my numbers are definitely not on OP's level, that is an impressive level of compensation.
There are a couple ways to do this. The easiest is to work with a good recruiting company. Lots of them suck but if you can find a good one it's worth it. Ask people you know for recommendations. If you find a good recruiter they will be familiar with how long each company takes so they can do things like have you start interviewing at places that take longer first. Essentially, they'll handle most of the timing issues for you. Having multiple offers puts you in a stronger negotiating position and they usually get paid a percentage of your starting salary so they want you to do well.
If you're doing it on your own the key is to apply to several places and communicate a lot with each company's internal recruiters. When you start interviewing ask what the whole process is and what the usual timeline is for each step. After each step send a brief thank you message. If they are slower getting back to you on the next step than you expected send a quick message to check on when you can expect to hear from them. As you're going through the process at various companies some will progress faster than others. Make sure that the slower ones are aware you're further along in interviews at other companies so they can catch up. When faster companies propose dates for the next step choose something in the longer end of the range to slow things down. Once you have your first offer inform the other companies you're interested in that you have an offer and they need to start wrapping things up one way or the other.
Most companies can be flexible about their timelines. Even places that are known for long application processes can be significantly sped up if they know you're on a deadline.
One way is to go back to your original company and say you're leaving. You then either sit back and see if they offer you more money to stay, or you explicitly tell them "NewCo is offering $X" and see if they match or beat that.
This move, while very gutsy and sometimes very effective, only really works in an industry where you're in high demand and/or you're essential to the operation of your current employer.
But, in either case, there's no guarantee. Your old boss might certainly counter-offer and give you the higher salary, but only long enough to find a replacement employee at (or even less than) your old salary. Then your salary very abruptly drops to $0.
When I look for a job I apply to multiple companies at the same time when I find job openings that match what I'm looking for and also apply to companies I'd love to work for that don't have openings.
So I end up having multiple phone interviews and then on-site interviews until I get one or more good offers. Just recently I got 3 really good offers in the span of two weeks and took the time to chose the one I really wanted to accept. I told each company I was interviewing at other places too and wanted some time to think.
(Of course if they're not interested in you anyway it doesn't matter how many offers you have.)
Remember, recruiting is a job too. The people who do it at the company want to hire you, they want to get those positions filled, that means they are doing their job well.
Or you can just lie about it, as OP did. Perhaps a risky maneuver, but if it's plausible for you to be in demand, I don't see why it's not worth trying.
Personally my approach is a bit more basic. I ask for what I want, and if you don't wanna give it to me then fine, someone else will. But, my numbers are definitely not on OP's level, that is an impressive level of compensation.