US citizen travelling to the UK with an immigration hiccup in the past

I am a US citizen currently living in France with a long-term researcher visa. In the next year, I need to visit the UK for the following purposes:

• A week-long meeting / informal training with collaborators at a UK university. [My question here is whether this would be classed as work...]

• Giving a talk at a UK scientific society in order to accept an award I have been given, in May.

• A week-long conference in June. I'd like to travel for a few days longer to visit my old city/friends, but only if I'm allowed to.

As a US citizen I can enter the country visa-free on discretion of the border agent. However, this is complicated by the fact that I lived in the UK as a student from 2010 to 2015. I had a problem upon returning to the UK after visiting my family in June 2015, because the date of my graduation had passed (it was less than a week before I made a visit home). My visa was valid until October (they give students an extra few months after graduation to get their affairs in order), so I assumed I was within my rights to come back, pack my stuff, get my French visa and move, but they told me that it was no longer valid since I had already graduated.

I had been planning to pack my things and move to France, as I had already accepted my position by then, and I was currently waiting for my French visa to be validated (moving directly from GB to FR is a lot less expensive than going by way of the US). I was detained for a few hours, and the only reason I was let into the country was because I showed them the offer for my French position which convinced them that I had sufficient motivation to leave the UK. I was told to be out of the country by the end of the temporary leave they issued (the ending date was in January 2016, and I left in October 2015).

I understand that the leave to enter can allow for multiple entries into the UK over the course of six months, provided that the visa holder does not exceed 180 days per year or do illegal things, such as working. None of my visits will be longer than 1½ weeks, but they will be spread out over the course of the six months mentioned. I am worried that the UK Immigration folks will wonder if I'm secretly living in the UK given the frequency of the visits, even if they are short visits.

Can I enter the UK under this ruleset for these visits again, or will I have a problem with this since I entered under that same program in June 2015?

Meaning: Would it be a better idea to apply for a formal visa for my visits?

If I can enter visa-free again, will the fact that I have no exit stamp from October 2015 (I moved via a lorry using the ferry, and there was NO passport control from Dover to Calais; trust me, I ran around looking for somebody to stamp me for ages) present an issue?

(To clarify, my passport was taken by the ferry operator, but I was told there would be no stamp on the UK side and there was zero French Immigration monitoring in Calais)?

I have a Schengen visa and a French residence permit, but since the UK isn't Schengen, I know that is useless.

I'm worried about the UK government assuming that I've overstayed since they will obviously have no record of me leaving. I have my ferry ticket receipt, but not sure if that's anything they'd care about.

Should I be applying for a standard visitor visa instead?

If so, for how long?

Does casual training with collaborators in their university count as 'work'?