To be truthful, I have not listened to the JJ longplate ecc803s, but from what I have heard via online gossip they are supposed to be highly regarded. Why not? Costs about as much as a case of beer, that's cheap compared to your Mesa.
As far as el34's go, I like JJ e34l. Depends on what the amp likes more than the user's prejudices... I thought that the svetlana's I have were too bright and the distortion was not as musical.
The best thing to remember about acquiring NOS or VOS tubes is to be patient and don't get all on them at once! If I was in your shoes I'd go ahead and start perusing auctions of those suggested types anyway. Get one new one per month or every other month, on the weeks where bils are lowest. It's all about being a buzzard, hover over the auctions and swoop down in the last little bit to bid. Fwooosh! Lots of deals are done on Sunday evenings, but I have gotten some screaming deals by bidding on items that did not close at prime times.
Also, if you don't use metal tone amounts of gain, vintage 12at7's work great in clean or dirty channels, they sound wonderful and can be had for dirt cheap, like 5-25 bucks each from a wide variety of makers plus shipping. There is a ton of gain in the circuits of most Mesa amps. Don't have to get the uber spendy cork sniffer ones to get great tones out of vintage at7's.
WAY too many guitar players are hung up on 12ax7's and some on 5751's...a 5751 is 70% of the gain of a 12ax7 and an at7 is 60% of the gain of a 12ax7, that 10% difference between 5751 and 12at7 is small in the amp/ear relationship. Look for a 12at7wa, wb, or wc, 6201, ecc81, e81cc, ecc801s, 6060, all those are 12at7 types, sound great and are surprisingly inexpensive for the most part. Tough to beat the bang/buck of a 12at7wc JAN Philips. If you want a brighter tone try a 6201 GE. Both can be had less than 10 bucks each. What you don't like you can get rid of. Those suggested tubes are both military issue, they are of top quality in construction, nobody builds them as well today. The new producion ones can be more expensive than vintage ones carefully purchased.
Save your Mesa tubes, do not get rid of them if your amp is under warranty.