The fit looks better than the red speedos although the fabric looks like cotton, suggesting they are underwear rather than swimwear.
I still suggest a brief or bikini with a pouch that will raise and bring forward your package presenting it better. Although extreme some of the Koala designs do this and should be reviewed for ideas.

Have you tried these?
 

https://www.amazon.com/gp/aw/d/B004N...BxL&ref=plSrch

Speedo suits tend to flatten the front. These don’t. The lighter colors may not be family friendly, but I’ve had no problems wearing the darker suits anywhere.

Would you like to try put on a C-ring or hair band, just to lift up the package a bit ?

Nice pouch brief snakeherder, but I was thinking of something with more lift.
Maybe like this :
https://www.amazon.com/DESMIIT-Mens-...7B938GP4J&th=1

A smaller package would be better, but I actually enjoy the squeeze of fitting into Japanese Aqux suits http://aqux.ocnk.net/ or Korean Mategear suits http://aqux.ocnk.net/, especially the flat front styles. Their suits are a size or two smaller than US sizes, so check the charts. Both are set up for easy ordering from USA.

Thanks
 

Thanks for all the suggestions! Perhaps I do need to consider one of these Asian brands or some kind of smaller bikinis. Lord knows that I don't fill out regular Speedos.

I just don't think I have the right body for such suits... My small package may fit, but not my body... I feel like my white bum would be hanging out the bottoms.

If you like it, wear it. I have been told that my skin tone is too light to wear yellow swimsuits. I wear them anyway, because I like how I look in them.

I have a few Asian-style suits I received from a fellow member of the board (Merci Louis). They're not as extreme as Mategear, but they do show a bit of cheek. I'm usually more of a thonger, but I'm sure they'll be worn often

If you want to continue wearing your current speedos but want to show more package you could consider wearing a jockstrap or thong under your speedos.
There are jocks and thongs designed to push your package upwards and forwards making the most of what you have. Avoid natural fibres as they wil go soggy when wet.
Maybe something like this:
https://www.ebay.co.uk/itm/Men-Athle...item41c28cf136
or:
https://www.ebay.co.uk/itm/Mens-Brie...hFzo ooxXcG9g
or:
https://www.ebay.co.uk/itm/Camouflag....c100005.m1851

Your second photo looks like a Speedo Solar in heather or gray. The Solar is the "pouchiest" Speedo brief, lets everything hang rather low. It's really the "odd man out" in the Speedo line-up.

You would fit better in any of the racing Speedo briefs with a 3" side. This would hold you more up and out, although a little flattened. You could get the classic Core Solid Lycra brief (style 70800). Or "The One" brief in Endurance Lite, which has more like a 2.5" side, and comes in lots of colors.

You can use a cloth tape measure to determine your Speedo size. Measure four finger widths below your navel. Ignore your pants size, there's serious vanity sizing in pants.

Thank you for the great advice! I think you have me convinced...I like the solar because it is kind of skimpy, but I don't appear to fill the pouch at all. I will try "the one."