Here's an idea for Spanish... I started out by thinking that <tt> = /t͡ʃ/ would fit in pretty well with the current spelling system, which has <ll> = /ʝ/~/ʎ/ and <ñ> = /ɲ/. As an added bonus, it even makes the connection to the Latin, French and Italian forms more obvious (the spelling becomes the same as Italian cognates, and the <t> is present in the Latin and French cognates).
Moving on from there, <ch> is now freed up to represent /k/ before <e> and <i>, which means we can use the analogous <gh> for /g/. This frees up <gue> and <gui> to be used in a parallel manner as <cue> and <cui>, and makes <gü> unnecessary.
The alternation between <c> and <z> for /θ/ will be preserved, as it is basically totally predictable (<zi> and <ze> are not used AFAIK).
It seems obvious to me to drop silent <h>, though maybe there's some reason not to that I haven't thought of (or maybe it looks stranger to native speakers).
The trickiest sound I think is /x/. The first thought I had was to regularize it along the lines of <c~z>, so that <g> is consistently used before <e> and <i>. However, I think this looks odd for some words. The most obvious option is to just use <j> everywhere, but I don't like how that looks. More options are shown below:
current: genealogía, México/Méjico, jejeje, jefe, jamón, reloj
all-j: jeneolojía, Méjico, jejeje, jefe, jamón, reloj
maximal g: genealogía, Mégico, gegege, gefe, jamón, reloj
all-x: xeneoloxía, México, xexexe, xefe, xamón, relox
all-h: heneolohía, Méhico, hehehe, hefe, hamón, reloh
I like the last one, but I think I'm probably biased as an English speaker.
And I guess replacing all <v> with <b> makes sense and looks OK as well, so let's go with it.
Here's a random respelled Wikipedia text sample:
(Here's it with "h" instead of "x," since some people indicated they thought they would prefer that)