No where does the Bible say "you may not work in civilian service" just like no where does it say "you may not vote".
While I agree with most of what you say, I would be wary about stating that Christians today can legitimately either vote for governments or serve in the military, without risking making themselves "part of the world".
All the examples you cite of working in high government office, directly influencing political affairs, are from the Old Testament, when God was using a specific nation on earth and also using the tools of human governance (eg: wars, political intrigues) in order to support that nation. So as you say, he placed individuals directly into roles for them to manoeuvre and influence events.
Since the arrival of the Messiah (the appointed King of God's Kingdom), the Scriptures show that God explicitly is not favouring or using a specific nation state on earth now (and has in fact purposed to wipe out human governments), so Christians should be more careful about matters that directly involve political affairs. The state of the world today shows the wisdom of keeping involvement more at arms-length, to avoid being caught up in bitter politics, bloodshed, etc (just look at Ukraine, Gaza-Israel, etc, etc!)
Regarding voting, this is clearly a position where an individual is choosing to endorse a particular political party to rule (even if just for a few years), unless they choose to enter the polling booth and spoil their ballot paper. That means that by voting, whether you like or accept it or not, you are endorsing all that that party stands for, against its rivals. You bear a share of responsibility for what it does (both good and evil) if it comes to power.
Serving in a job within civil administration is not necessarily the same (for example the UK's civil service or a similar administrative role) as you are not explicitly favouring a particular party ideology, in the same way that paying taxes (which may be used in part to fund non-Christian things such as weapons) is not the same as directly working in a factory that builds munitions. To my knowledge there is no indication of any Bible Christian voting for a human leader or ruler (such as in the Roman Senate or equivalent administrative body).
Regarding military service today, bear in mind that Christians are prohibited from deliberately killing others. This rules out serving in a modern-day military, since being trained and used to kill others is a key part of the role. In contrast, roles like riot control, investigating crimes such as theft, murder, and other civilian duties do not require the need to kill, so a role in a civilian police force or civil/home guard is potentially more acceptable.
In Bible times, all these civilian duties were also performed by elements of the military as there was no such thing as a formal civilian police force, so at that time there would have been no distinction. So with regard to someone like Cornelius, once converted to Christianity, he could have transferred to (or perhaps was already serving in) a more 'civil' capacity as a guard or administrator/trainer/etc, but still retain his rank and position in the Roman military.
So today, I would draw the distinction between serving in the military (where a willingness to kill is essential) and serving in a civil guard or police role (where it is not), in terms of your likely exposure to behaviour that could violate Christian standards.
