Hi Vadim! Lojban, lol - yes you are a geek then, aren't you !
I think I may be similar age to you, about..... and I also work in IT (project manager, but I have been a programmer in the past).

Your English in your post above is very good. If you write this without thinking too much about what you wrote, then you have nothing to worry about.

The thing to remember about IT is that most IT people, even in English speaking countries are not actually native English speakers. I live in London, but I am Swedish. My almost unnoticeable accent does more good than harm. That's the way to approach English in IT.

A lot of people I work with right here in the UK are Indian, some of African background. In the past I have worked with "outsourced" and other foreign colleagues across all of the EU and in Israel, Ukraine, Malaysia. So anything goes.... As long as people understand what you are saying, and you can understand what people are saying to you, then there is no problem.

And many IT people who ARE native English speakers are useless at grammar and spelling. Without bragging, I am almost invariably better at writing in English than native English speakers in my teams (programmers). I don't know why, but it's definitely possible to have a university degree in the UK and still have lousy grammar and spelling. It's the norm rather than the exception in IT. My impression is that the situation is no different in the USA.

For a management job you need to be able to communicate well in English though, not accidentally say something rude, and handle the "niceties". So if that's where your ambitions lie, then you are right to really make an effort. However, if you can speak like you write you are making great progress.

The style and way of speaking (not just accent) varies quite a bit between Brits and American. So depending on which country you work more with or relate better to, you might want to focus on that way of speaking, and not the other. I recommend British English, of course!
However American English and the way that Americans express themselves in general, and behave at work, is quite different to the UK, so if that's your main point of contact with the English speaking world, then you might want to tap into the US way of speaking English.