I have an English sentence that I need to switch the word order of so I can translate it into my conlang smoothly, but the sentence is pretty complex and I’m not sure how to go about it. The sentence is “ I feel like he would like to try it after then.” I would like to switch the word order to SOV. Thanks in advance!
Perhaps the best way is to transate it into a different natlang, preferrably one with the intended word order.
While German is not your typical SOV language (what is typical, after all?), it is close:
Ich habe das Gefühl, dass er es danach gerne versuchen würde. 
Note there are aready some idiomatic differences from English: "to feel like" is "das Gefühl haben", i.e. "to have the feeling", and the subordinating conjunction is obligatory (as in majority of European languages). Also note that "to try it" is kind of ambiguous in English.
To turn it into a better SOV sentence, let's rearrange the word order a bit:
Ich das Gefühl habe, dass er es danach gerne versuchen würde.
No longer syntacticaly correct German, but a good start for the translation. Also note that word order classification does not creeate hard constraints - especially in complex sentences, some constituents just like to stick together or to the clause boundaries. So we can turn it into:
Das Gefühl habe ich, dass er es danach gerne versuchen würde.
which in fact is again better German (a bit poetic perhaps).
Remove pronouns as fit if your conlang is a pro-drop one, and you can start translating...
 corrections are welcome, this is just my best bet
 let's try the sentence in Slovak: "Mám pocit, že by to rád potom vyskúšal". (have-1P-SG feeling-ACC that-CONJ would-AUX it-ACC like-MSC then try-PAST). Almost perfect SOV, despite Slovak being prototypically SVO. Note that the "by" auxilliary particle turns the verb into a conditional, but it does not have to be next to the verb itself. And as a very happy pro-drop language, there are almost no pronouns left, and the word order is quite fixed (changing it would remain grammatical, but bring emphasis to different parts of the sentence)
Presto Didgo Abbaca da Barabba Ortem Changeo!
“I feel like he would like to try it after then.”
I as if he would like to try it after then feel.
This example changes the main verb only, leaving the relative clause SV.
I as if to try it after then would like he feel.
This example makes the main clause SOV and the subordinate clause OVS.
I as if he to try it would like after then feel.
This one changes both the main and subordinate clause SOV.