Note that the p and span tags you've added are superfluous. The span tag is used to modify a character, a word or a phrase inside a paragraph: you don't use it to modify a complete block. The p tag is used to modify a paragraph: you don't need it when you want to modify a larger block. In other words, you'd need these tags if you wanted to modify parts of the bq; in this case your additions should be part of the bq style. Instead of this:

<blockquote style="border-radius:10px;font-size:175%;font-weight:bold;background-color:#eaf5f4;margin-bottom:1.1em;padding:1.3em 1.1em .09em;">
<p style="text-align:right;"><span style="color:#e2c10b;">
TEXT HERE</span></p>
</blockquote>

you write this:

<blockquote style="border-radius:10px;font-size:175%;font-weight:bold;text-align:right;color:#e2c10b;background-color:#eaf5f4;margin-bottom:1.1em;padding:1.3em 1.1em .09em;">
TEXT HERE
</blockquote>

If you check my blog, you'll find an introduction to HTML and various posts on formatting text etc: they might prove useful to you. (And I'm glad that unlike most users you're not intimidated by coding!)

TEXT HERE

You can play around with the values, or ask me if there's something you'd like to change and don't know how.