Time (and a place) for an odd-one-out puzzle

Question

_{This puzzle is part of the Monthly Topic Challenge #6: Is it really that [time] again?.}

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It is a tough task to create an 'odd-one-out' type puzzle whose solution lacks any ambiguity at all - it is all too easy for a second unintended pattern to lurk within a small number of options. To attempt to overcome that (without making the set of options a ridiculously long list), here is a puzzle where the solver is asked to find the 'odd-one-out' in eight different sets where the reasoning behind what makes an option the odd-one-out is identical for each set.

Moreover, once these sets are resolved you should be able to answer the question: The name of which 8-letter country is concealed within this puzzle?

W	Assumption, Large River Inhabitants, Saint James, Warm Location
H	Admiral of the Fleet Sir Fairfax, Beach, Island of the Empty Voyage(*), Ngambri
E	Adjacent to the Water, Forested Land, Holy Saviour, Sandalwood
R	Eastern Capital, Flat Land, I Saw a Mountain, Place of Fermented Mud
E	He Does Not Sleep, Port Town, The Victorious, Wisdom
A	Crocodile River, Québécois Prospector Joe(*), Smoky Bay, Where People Get Honour and Respect
M	King George III, Mrs Penh’s Hill, Our Lady of Peace, Saint Dominic
I	Big House, Monday, Stone City, The Passage (of the Lagoon)

Answer 1

You are in ...

... Portugal.

Step I: Geography

The items in the list describe the meaning of the names of various national capitals. At first, I tried to work my way through the list of capitals on Wikipedia, but then I found a page that explains the etymologies of these capitals, which was a huge help.

Anyway, the capitals are:

Asunción, Paraguay;
Paramaribo, Suriname;
Santiago, Chile;
Tbilisi, Georgia

Port Moresby, Papua New Guinea;
Praia, Cabo Verde;
Saipan, N. Mariana Islands;
Canberra, Australia

Managua, Nicaragua;
Guatemala City, Guatemala;
San Salvador, El Salvador;
Vientiane, Laos

Tokyo, Japan;
Pyongyang, North Korea;
Montevideo, Uruguay;
Ngerulmud, Palau

Harare, Zimbabwe;
Port Vila, Vanuatu;
Cairo, Egypt;
Sofia, Bulgaria

Bamako, Mali;
Juneau, Alaska;
Reykjavík, Iceland;
Ouagadougou, Burkina Faso

Georgetown, Guyana;
Phnom Penh, Cambodia;
La Paz, Bolivia;
Santo Domingo, Dom. Rep.

Malé, Maldives;
Dushanbe, Tajikistan;
Tashkent, Uzbekistan;
South Tarawa, Kiribati

(An asterisk on the items means that the capital is not one of a sovereign state.)

Step II: Odd-one-out and Time

Now to find the odd ones out in each group. The theme of the monthly challenge helps us here: We need to find the time zone of each capital.

We'll see that only three cities in each group are in the same time zone, so we've found the odd one out:

W:   −4 except Tbilisi at +4
H:   +10, except Praia at −1
E:   −6, except Vientiane at +7
R:   +9 except Montevideo at −3
E:   +2, except Port Vila at +11
A:   0, except Juneau at −9
M:   −4, except Phnom Penh at +7
I:     +5, excapt South Tarawa at +12

Step III: Anagram

One thing we haven't used yet is the letters before each set that spell out "Where am I?". The time difference to Greenwich time for the odd one out in each group gives us an offset to these letters. For example, shifting W four places to the "east" gives us an A, because the alphabet wraps after Z.

We get AGLOPRTU, which we can anagram to the answer, Portugal.

Appendix: Worksheet

For what it's worth, I've pasted my "worksheet" below. It's the final state of what I had in my text editor while gathering information and trying to work out what goes on. It should be the same data as described in the steps above, but it's all in one place, which is nice, I think.

W   Assumption                               -4 Asunción, Paraguay
    Large River Inhabitants                  -4 Paramaribo, Suriname
    Saint James                              -4 Santiago, Chile
    Warm Location                       A *  +4 Tbilisi, Georgia

H   Admiral of the Fleet Sir Fairfax        +10 Port Moresby, Papua New Guinea
    Beach                               G *  -1 Praia, Cabo Verde
    Island of the Empty Voyage(*)           +10 Saipan, N. Mariana Islands
    Ngambri                                 +10 Canberra, Australia

E   Adjacent to the Water                    -6 Managua, Nicaragua
    Forested Land                            -6 Guatemala City, Guatemala
    Holy Saviour                             -6 San Salvador, El Salvador
    Sandalwood                          L *  +7 Vientiane, Laos

R   Eastern Capital                          +9 Tokyo, Japan
    Flat Land                                +9 Pyongyang, North Korea
    I Saw a Mountain                    O *  -3 Montevideo, Uruguay
    Place of Fermented Mud                   +9 Ngerulmud, Palau

E   He Does Not Sleep                        +2 Harare, Zimbabwe
    Port Town                           P * +11 Port Vila, Vanuatu
    The Victorious                           +2 Cairo, Egypt
    Wisdom                                   +2 Sofia, Bulgaria

A   Crocodile River                           0 Bamako, Mali
    Québécois Prospector Joe(*)         R *  -9 Juneau, Alaska
    Smoky Bay                                 0 Reykjavík, Iceland
    Where People Get Honour and Respect       0 Ouagadougou, Burkina Faso

M   King George III                          -4 Georgetown, Guyana
    Mrs Penh's Hill                     T *  +7 Phnom Penh, Cambodia
    Our Lady of Peace                        -4 La Paz, Bolivia
    Saint Dominic                            -4 Satnto Domingo, Dom. Rep.

I   Big House                                +5 Malé, Maldives
    Monday                                   +5 Dushanbe, Tajikistan
    Stone City                               +5 Tashkent, Uzbekistan
    The Passage (of the Lagoon)         U * +12 South Tarawa, Kiribati