Laos only has single entry tourist visas . There is no requirement to be out of the country for a specified time before you can come back again.
It's as easy to do it yourself and quicker sometimes also. Bus goes from central station in Chiang Rai. Sometimes he'll go straight to the border post, other times (depends on how many locals on the bus) they drop you at the junction where there are tuc tuc drivers to take you to border post. Once Thailand is exited there is a bus to cross no mans land through to the Laos border and again tuc tucs to take you into the town or to the local bus station. I was charged 45$ to get into Laos last week the river gathered all our passports and insisted on doing all the work. This was from Cambodia. Bring enough $$
As mentioned above (excuse the repetition) check out Hobo Maps Travel Info for Huay Xai. It's a good resource for recent info contributed by independent travelers. Note: Huay Xai is often referred to as "Bokeo" (pronounced "baw-gao").
http://www.hobomaps.com/TravelCKHX.html
"Chiang Rai to Bokeo Buses - buses depart from Bus Terminal 2 in Chiang Rai and take passengers over the Mekong bridge and thru immigration at both sides, then continues 5 km more to the Phetaloun Bus Station in Bokeo Province ... Costs 220 baht. In November 2018 there were 2 daily scheduled departures at 10:00 AM and 16:30."
Remember to bring USD$30-40 (depending on nationality) for Lao visa on arrival. You can pay in Thai Baht but at a bad conversion rate.
I think the package tour poster #3 was trying to describe is this: https://www.travelhubchiangmai.com/tour-detail/tl3001-3-day-2-night-slow-boat-package.html
Even if you buy one of these package tours involving various different transports the whole way through, it's definitely not worry free. You change transport providers enough times it's easy for something to mess up, and you wind up waiting too long or getting into an argument.

From Hobo Maps website is the following " From Bus Station 2 in Chiang Rai - PLS Company buses are scheduled to depart at 10:00 & 16:30 every day and take passengers over the Mekong bridge and thru immigration at both sides into Laos at Bokeo. Sometimes the 10:00 bus departs early so be at C. Rai bus station by 09:00 to be sure. It's a 3 hour bus trip on a nice big air conditioned bus. The bus fare is 220 baht."
These buses take you to Phetaloun Bus Station about 5 km into Laos and from there it's a 6 km trip to Huay Xay town by tuk tuk or songtaew style bus.
The last time I made this trip, there were direct buses (two a day I think) taking you straight from one of Chiang Rai's main bus stations (I can't remember which one) to Huai Xai. They weren't particularly expensive, and were comfortable, Thai buses. I got information on the buses by enquiring at the central Chiang Rai bus station, in the middle of town (though I don't remember if that's the bus station that the buses left from).
It's been a few years, so things might have changed, but I imagine there's still a direct bus service. Note that Laos has an issue with building bus stations far from town centers, so the bus will probably drop you off a fair distance from the middle of Huai Xai. I'm not aware of current details though.