Jifrisco, your first option requires a US practical test with a pilot examiner or FAA inspector rather than an IPC. Your existing instrument flight time, including instrument flight time under instruction, ought to be countable iaw 14 CFR 61.41. Assuming it's for the airplane category, only the IRA knowledge test counts under this option. The second option has the advantage of avoiding the need for a US medical certificate. If you are so inclined, it could be worthwhile applying for this in addition to a standard IR. The third option, a conversion pursuant to the EU-US conversion agreement, only applies to licences and ratings issued by an EU country.
The conversion option has the major advantage of avoiding a US practical test with an pilot examiner or FAA inspector. It can also be pursued without needing to undertake instrument flight training, save for any recurrent training needed to pass the IPC. The TIP-L requires the IPC to be done before applying for the rating. The same is true for the flight review, which must be done before applying for the standard US private pilot certificate.
The TIP-L at para 2.3.5, point (a)(ii)(2), states that you can avoid needing to acclimatisation (training) if you have "[p]rior experience of at least 10 hours of flight time under IFR as PIC on airplanes in the United States gained after initial issue of the [EU Part-FCL] IR(A)." The FAA interprets "under IFR" as meaning "instrument flight time," which means flight by sole reference to the instruments done in either simulated or actual instrument conditions. Under 14 CFR 61.51(e)(1)(i), you may log this flight time as PIC if you are the sole manipulator of the controls (etc). This means you can fly these ten hours in simulated instrument conditions in the United States, with a safety pilot, without invoking the need for a TSA security threat assessment, because no instrument flight training will have been received. Otherwise, unless you're a US national, you'll need a TSA security threat assessment before receiving training towards the instrument rating from a US flight instructor, regardless of where in the world it's done.
You are right that the specific knowledge test must be done in each case. In other words, the regular IRA knowledge test only counts for a standard IR sought by way of a US practical test. The IRA does not count for the IR obtained under the EU-US conversion agreement, nor for the restricted (foreign-based) IR issued iaw 14 CFR 61.75.
Foreign pilot verification requests can now be made through IACRA. You can also use IACRA to apply for a standard US private/instrument pursuant to the EU-US conversion agreement. Pick whichever FSDO suits you. You can easily nominate a different FSDO later.
If you wish to undertake training, you'll probably need an M-1 (non-academic/vocational) student visa. You won't need a visa merely to write a knowledge test or attempt an IPC. Recurrent training on small aeroplanes won't require a visa or TSA security threat assessment either.