I think synergy makes all the difference, and all the tubes in the Torii matter. So I just put in the stock 6N1Ps that came with mine as a point of reference for heading into a sweeter "romantic" sound. Right now I am using RCA 5U4G-ST (coke bottle.... off branding cheap from brent jesse), cryo'd Ruby EL34BSTs (Shuguang/not treasures), RCA OA3s and RCA OC2s. From this, I will change only input tubes for this comparison.
But no matter what inputs you use, something very useful with the torii is the reg tubes. OA3s to OB3s or OC3Ws will lower the grid voltage opening things up without extreme signature shifts. Or, for an input tube shift, you can change the OC2s to OB2s directly "tweaking" the input tube sound toward more detail/less warmth. So depending on the objective, if the general sound is good, you can really tune it to taste with the regulators in a really inexpensive way.

Then there are feet and tube dampers. The first thing I noticed with the 6N1Ps is that they are richened/smoothed up a notch by putting herbiesaudiolab RX tube dampers on them. In my experience, these tube dampers and herbies isocup feet w/lampblack balls level the playing field of tubes. By cutting vibration and microphonics tubes tend to sound better while making them more readable. My feet have stainless basses and actually I am using two w/lampblack balls and two w/picture jasper balls under the Torii at the moment...a bit more focus and detail than lampblacks alone). I don't use tube dampers on all the tubes. Like now I don't have them on the back EL34s, or the regulators. I try to hold the a fine line between things getting so smooth that I lose musicality.
Anyway, I replaced the 6N1Ps with some "premium" national 7DJ8s, and what I heard first was more power! So I turned it down. Then I heard increased dynamics, space, texture, definition and a slight bawdy openness quality that I like as it tends to pull a "liveness" from the sound. That could perhaps move them into the romantic depending on how you look at it....definitely more everything good, but with a similar richness as the 6N1P. The only down side might be that they could be thought of as a little brash and unrefined. But then I put on the RX dampers, and this refined them notably. I like this tube, but I like an open live sound. So I think this tube will probably not be a mistake. Just might be worth a look at the RX dampers and perhap feet if they are a little brash after burnin.
Another tube in a similar arena is the Matsushita/National 6922 (also Mullard tooling) from tubemonger 80 for a pair.....warmer, with more of the 6922 solidity....I would say more even mannered than the national 7DJ8, though I don't suggest this as necessarily a better trait, just different. Also I have a pair of Mullard CV2492 E88CC 6922 - M. Pairs USED 1969-1978 Dimple Disc Getter - Gt. Britain also from tubemonger. At $75 a pair, this is a good way to try the famed Mullards without too much investment. And unlike some tube companies, tubemonger's sets are all well matched ('Premium" or better) unless marked with "imperfect scores." I find these Mullards sort of in between the two japanese tubes with the sort of even refinement of the 6922 and a nice, (though slightly more refined) open clarity of the 7DJ8, and they are couched in a classic warmth. It is a detailed warmth without too much sense of a darkish veil....a "warmth" I prefer. Probably a decent choice if the 7DJ8s are not quite refined/sweet/warm enough

Lastly, In the quest for romance, I wanted to look at Amperex. I put in some Bugle Boy pulls from nostubestore.com. @$64 a pair (before shipping from Turkey), a cheap way to try really nice NOS tubes. I have always loved aspects of these tubes.....their soft, but detailed and musical character. Like the Mullards, warmth without veils, but also with a micro detail I really like from good 6DJ8s. Also in the Amperex vein, the orange globe/a-frame 6DJ8 pulls (56/pr from nostubestore) ...definately the Amperex micro detail and brighter upper midrange than the Bugle Boys, but quite a bit in the same family. I really like Amperex tubes, and the 6DJ8s in particular have a nice warmth we might call romantic. These may be worth look too if you feel the need to roll the 7DJ8s. My input tube of choice lately is a pair of early 60s Philips/Amperex 6922/E88CC SQ, also from nostubestore but not listed on the site. Very transparent, refined, open, smooth and warm without loss of detail. But they were 90 each. Koray at the nostubestore, is a really good resource by the way if you email him.

All of these are nice tubes that I suspect would do good things toward bringing in that sort of real/live sound that we might count as sweeter and richer, and to me, all have notable improvements over the 6N1P. And again, these comparisons are just changing the inputs. I will often change the regs, rectifiers or power tubes to refine things.
Also again, with this many tubes in a Torii, vibration is a thing, so if this is not solved in your system, I think the herbies stuff is well worth a look/try (90 day return) making tube rolling no less fun, but a little less important.