After exchanging the $3\text{rd}$ and $6\text{th}$ letters, the $4\text{th}$ and $9\text{th}$ letters, as well as the $5\text{th}$ and $10\text{th}$ letters in the given jumbled letter series, which of them would result in a meaningful English word?
I. HRETIAGVSN
II. FLNESAGOMI
III. EXSONHTIAU

Let's systematically perform the letter swaps for each option:
Swaps: $(3\leftrightarrow 6)$, $(4\leftrightarrow 9)$, $(5\leftrightarrow 10)$

* Series I: H R E T I A G V S N
* Positions: 1:H, 2:R, 3:E, 4:T, 5:I, 6:A, 7:G, 8:V, 9:S, 10:N
* Swap 3 & 6 (E $\leftrightarrow$ A) $⟹$ H R A T I E G V S N
* Swap 4 & 9 (T $\leftrightarrow$ S) $⟹$ H R A S I E G V T N
* Swap 5 & 10 (I $\leftrightarrow$ N) $⟹$ H R A S N E G V T I
* Word formed: HRASNEGVTI (Not a meaningful word).

* Series II: F L N E S A G O M I
* Positions: 1:F, 2:L, 3:N, 4:E, 5:S, 6:A, 7:G, 8:O, 9:M, 10:I
* Swap 3 & 6 (N $\leftrightarrow$ A) $⟹$ F L A E S N G O M I
* Swap 4 & 9 (E $\leftrightarrow$ M) $⟹$ F L A M S N G O E I
* Swap 5 & 10 (S $\leftrightarrow$ I) $⟹$ F L A M I N G O E S
* Word formed: FLAMINGOES (Meaningful word, plural of flamingo).

* Series III: E X S O N H T I A U
* Positions: 1:E, 2:X, 3:S, 4:O, 5:N, 6:H, 7:T, 8:I, 9:A, 10:U
* Swap 3 & 6 (S $\leftrightarrow$ H) $⟹$ E X H O N S T I A U
* Swap 4 & 9 (O $\leftrightarrow$ A) $⟹$ E X H A N S T I O U
* Swap 5 & 10 (N $\leftrightarrow$ U) $⟹$ E X H A U S T I O N
* Word formed: EXHAUSTION (Meaningful word).

Therefore, both series II and III yield meaningful words.