Wow - these misconceptions still going around.
It's been about 15 years since I converted a jpeg to tiff for print.
Jpegs are fine in print, and you don't need to convert them to CMYK unless you are in colour critical conditions, then and only then I'd have a layered PSD or TIFF with the colour corrections so I can go back and fix the colour based on colour accurate proofs.
However, jpegs do have artefacts - they are DO NOT print - unless the jpeg image is severely degraded and they are physically noticeable on your screen or the image is far too low resolution.
For a 300 ppi image - a jpeg artefact won't show in print.
And even for most types of litho print you don't even need 300ppi.
PPI is derived in litho print from the LPI the RIP is set to. A decent printer would alter their RIP based on the quality of the print required. Art books would be set at about 175-200 LPI. Magazines and other things of such nature would be approx 150 LPI. And things like newspapers/rags etc would be set at 80-120 LPI.
You derive the DPI by multiplying the LPI x 1.5 (most people do x2 but it's overkill for very mathematical reasons).
Anyway - you may gather that most have their LPI set to 150 - hence 150LPI x 2 = 300 DPI.
NOW - if you're sending your file to a newspaper - they might have upped their game, but most newspapers are on pourous paper - so 120 dots per inch gives a nice spread - hey 80 dots per inch gives a nicer spread for that pourous paper, where the ink saturates into the paper and spreads out - hence having less dots per inch results in a nicer print for them, and doesn't soak the pourous paper with ink.
If you can imagine having 300 dots per inch packed in tightly like that on a pourous paper - it would saturate the paper as the ink soaks into the rag paper.
For art books the paper is a lot finer and it is not as saturate - so you can have 175 LPI x 1.5 = which is only 262.5 DPI! - not 300DPI.
Anyway - I'm getting away from JPEGS.
Converting to CMYK is an antiquated workflow from the Quark days - which simply doesn't need to be done (unless a colour critical workflow).
Your best settings for export to PDF is PDFX4a which leaves all your colours in the colour space they are originally.
The printers RIP then converts them to the proper CMYK profile for their RIP and printers - which is best for all around - as their RIP has a thing called Colour Lookup Tables (or CLUT or sometimes just LUT) .
Think about it - you have a JPEG file in RGB. You convert that to CMYK - now you have 2 files - a jpeg in RGB and a tiff in CMYK?
Why - your photoshop conversion of the CMYK is inferior to the RIP as the RIP is profiled for the printing press.
Not only have you got 2 files - and 2 sets of changes to the image if it's requested.
For about 15 years I've left all images (PNG GIF JPEG TIFF PSD etc) exactly how it was supplied. It's converted to CMYK in the RIP (best Place for it and all spot colours (again LUTs))
If you do a conversion of RGB to CMYK - and show that to your client - then you show them a CMYK profile that is not being used in print.
Your CMYK profiles are automatically ignored by RIPs (mostly) - and stripped out for the printers CMYK profile in the RIP for the printing machine it's being printed on.
If you need to show a CMYK proof to clients either get a RIPped proof - or get a RIPed printed proof to show them.
And don't worry about JPEGs in your workflow - they are fine - don't even bother converting them.
If you're printer comes back saying their's RGBs in your print ready file (or spots) then drop them and find a new printers - they are running antiquated RIPs and machines and probably old CLUTs - which is most likely not going to be able to decipher a modern PDF created with modern software.
If you really need to send it to them - then do a conversion to CMYK on output of the PDF from your software - which most Adobe software has - and use European Prepress 3 - as it's a generic profile and will convert all your colours to the generic CMYK profile.
I wouldn't ask an old school mechanic who only works on mechanical cars to fix a Tesla or a BMWX5 - they wouldn't know where to start.
Think about that.