what is my system's weakest link?

During my crazy days of changing equipment almost as regularly as my underwear I owned a pair of Thiel 1.6s. They were only a little larger than the 1.5s but they were so much better to my ear. Much smoother sound with deeper bass. Also much better looking IMO. You can find them for less than $1k used if you watch.
I still prefer the sound of the Vandersteen 1c in that size and price.
All of my searching was an attempt to better the sound of my old Meadowlark Audio Kestrels. My quest seemed to focus on time coherent speakers such as Thiels and Vandersteen. There are a lot of nice options out there but I gave up searching a couple years ago.

I don't think there is a consensus to change speakers.

Moreytalmor, this is a perfect example of why it's important to give as much detailed and concise information as possible when asking for opinions on this forum. First of all, remember that these are just opinions (ours) and it's yours that count to the most. However, without all the facts we are forced to read between the lines. For example: THE ONLY comment in your post re the kind of sound you like was the reference to the Mc preamp as being "warm". OK, I figured, the guy wants a warmer sound. Reinforcing that assumption was what I know about the sound of the Thiels; they are not what I would call warm. Now we learn that not only do you think they sound great, but you like the way they look and seem to be reluctant to give them up. That's great, and nothing wrong with liking the way gear looks. OK, if they sound great then that tells me that the amp/speaker synergy is probably not too bad for your listening habits and tastes (notice I am still reading between the lines).

So, what areas exactly are you feeling the sound of your system is deficient on? What are you looking for? More fullness (warmth), more detail, bigger soundstage, more volume? Or are you looking for simply an overall, general improvement in sound from "great" to really great. Also, does your budget of $1300 include the proceeds from the sale of whatever it is you end up selling? What cartridge do you have on your tt?

I've been watching this thread
and almost responded a couple times. I see much good advice without general consensus.

You like your speakers, so I would keep them. Many posters have indicated that power may be limiting to get the most out of them. This is true for Thiels. How true it is for you depends on room size and listening level.

You have a good entry level turntable. However I would consider it to be the weakest link. The signal never improves beyond the source. Generally entry level turntables are sold with a decent cartridge. However, the cartridge is one component that can be upgraded for a significant return on investment. With a vinyl system it is important to match the characteristics of the transducers, cartridge and speakers, to tune a system toward desired tonal balance. A cartridge upgrade may give you what you are looking for. A cartridge with a touch of warmth, not tipped up on the high end, with strong bass, and cohesive midrange might be in order.

I have not listened to cartridges lately so can't make specific recommendations. Sorry. Maybe others will chime in.

Amp power ratings help determine how loud and clear things can go in various size rooms, but there is more to what the right power amp brings to the table sound quality-wise.

Current delivery (peak amps) is a better indicator of how well an amp will drive more difficult load speakers like Thiel even at low volumes. Driving better at low volumes generally means better tonality, detail, articulation and most other things associated with good sound, a more natural and "effortless" delivery top to bottom. A 40 watt power amp with high current delivery will sound different and likely much better, all other things aside, than one with less, in the case of the Thiels.

Source improvements may be hard to assess if the bottleneck is the amps ability to drive the speakers to their max, even at lower volumes, due to limited current delivery, as is more typical with integrated amps than separate power amps due to the physical limitations imposed by having powr amp in close proximity to line level and even lower phono level circuits.. Once amp/speaker combo is in a good place, then one is in a better position to assess how well changes in source devices work or not, and it will be much easier to make improvements with that from there.

BTW, most speaker designs that target extended bass in a smaller box (a popular choice practically for many these days) is likely to be a difficult load for an amp to drive. Thiels are just one case. They are very good speakers. Just not ones that will perform equally well with just any amp.