If it is really annoying you then maybe you should do the swap, but my question was really to ask have you analysed why you want to. If it was just 'newer is best so I'll have that' then that's not a great reason but I see you have thought it through. I don't honestly think you can easily magnetise a modern watch all that easily unless you are working with a cyclotron on a regular basis so I honestly doubt you have a problem there. it might be running badly for a number of reasons but I doubt magnetic flux is the issue. I haven't magnetised a watch in 30 years and I have worked with some devices that have the capability to generate sizeable fields. if you have, you'll know since it will run very fast, not just a few seconds a day, more like minutes.
There are some downsides to changing, I don't personally like the new bracelet design, the less traditional and less balanced text layout and the increase in price. The step dial is a nice plus though so go with what you feel is best. Servicing is a bit of a red herring. The 1861 is easier for an Indy to work on but with the parts limitations even they will have problems before too long unless they have a parts account. I don't believe the 3861 has a longer service interval, the coax escapement doesn't magically make the other moving parts not need periodic maintenance.
Neither is a bad choice really.